I want to set the value of stream ‘PFD136’ to flow_136. Seems I have a syntax error. Please helpI want to set the value of stream ‘PFD136’ to flow_136. Seems I have a syntax error. Please help I want to set the value of stream ‘PFD136’ to flow_136. Seems I have a syntax error. Please help hysys, hysysinterface, setvalue MATLAB Answers — New Questions

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The blog Generative AI + Robotics = Awesome! says "you can reach out to us directly to request trial code access" yet there is no details of whom to contact or how. I feel I may be missing something obvious. Can anybody help me to get in contact with the Authors.The blog Generative AI + Robotics = Awesome! says "you can reach out to us directly to request trial code access" yet there is no details of whom to contact or how. I feel I may be missing something obvious. Can anybody help me to get in contact with the Authors. The blog Generative AI + Robotics = Awesome! says "you can reach out to us directly to request trial code access" yet there is no details of whom to contact or how. I feel I may be missing something obvious. Can anybody help me to get in contact with the Authors. robotics vla blog. MATLAB Answers — New Questions

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In App Desinger I want to add tooltips to each ui tree checkbox, so here each checkbox shall tell the user more of what is done or checked with the check exactly. Example: For "Block Colors" a tooltip might show something like "Checks if each Simulink Block has its dedicated color as defined by the company guidelines". Is there an option, as I can only find to add a tooltip to the parent CheckBoxTree but not each individual checkbox? Thank you.In App Desinger I want to add tooltips to each ui tree checkbox, so here each checkbox shall tell the user more of what is done or checked with the check exactly. Example: For "Block Colors" a tooltip might show something like "Checks if each Simulink Block has its dedicated color as defined by the company guidelines". Is there an option, as I can only find to add a tooltip to the parent CheckBoxTree but not each individual checkbox? Thank you. In App Desinger I want to add tooltips to each ui tree checkbox, so here each checkbox shall tell the user more of what is done or checked with the check exactly. Example: For "Block Colors" a tooltip might show something like "Checks if each Simulink Block has its dedicated color as defined by the company guidelines". Is there an option, as I can only find to add a tooltip to the parent CheckBoxTree but not each individual checkbox? Thank you. appdesigner, matlab gui, checkbox MATLAB Answers — New Questions

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I have a Matlab script that has worked fine in R2021b and earlier which I still use today. It simply reads my audio on a Macbook Pro running MacOS 12 and presents a spectrum on the analyzer. Moving that script to the new R2025b and modifying the script to call the new spectrum analyzer seems to work to present the spectrum but when I select "Measurements" and "Distortion" the distortion data appears but does not seem to find the main tone and in-turn the harmonics. I am stuck using the old version of Matlab since that works. I think I may be missing a configuration command on the new analyzer that wasn’t required on the old one. The tone below is on CH1 and CH2 identically. CH2 appears in front of CH1.I have a Matlab script that has worked fine in R2021b and earlier which I still use today. It simply reads my audio on a Macbook Pro running MacOS 12 and presents a spectrum on the analyzer. Moving that script to the new R2025b and modifying the script to call the new spectrum analyzer seems to work to present the spectrum but when I select "Measurements" and "Distortion" the distortion data appears but does not seem to find the main tone and in-turn the harmonics. I am stuck using the old version of Matlab since that works. I think I may be missing a configuration command on the new analyzer that wasn’t required on the old one. The tone below is on CH1 and CH2 identically. CH2 appears in front of CH1. I have a Matlab script that has worked fine in R2021b and earlier which I still use today. It simply reads my audio on a Macbook Pro running MacOS 12 and presents a spectrum on the analyzer. Moving that script to the new R2025b and modifying the script to call the new spectrum analyzer seems to work to present the spectrum but when I select "Measurements" and "Distortion" the distortion data appears but does not seem to find the main tone and in-turn the harmonics. I am stuck using the old version of Matlab since that works. I think I may be missing a configuration command on the new analyzer that wasn’t required on the old one. The tone below is on CH1 and CH2 identically. CH2 appears in front of CH1. spectrumanalyzer MATLAB Answers — New Questions

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Can I view the display connected to my Speedgoat target on my host computer to monitor the Simulink Real-Time (SLRT) simulation and take screenshots?Can I view the display connected to my Speedgoat target on my host computer to monitor the Simulink Real-Time (SLRT) simulation and take screenshots? Can I view the display connected to my Speedgoat target on my host computer to monitor the Simulink Real-Time (SLRT) simulation and take screenshots? slrt, targetscreen, statusmonitor, systemlog, console, log MATLAB Answers — New Questions

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Hi everyone, recently I started to work on PINN. I tried to apply Lie symmetries enhanced PINN (sPINN). For this purpose, I tried to train the Kdv equation in [1] with the same conditions. The problem is, in theory, sPINN must give a better approximation than classic PINN, but in my code, I think something is missing. I changed the initial condition, equation, and added the symmetry condition of the code in [2].
[1] Enforcing continuous symmetries in physics-informed neural network for solving forward and inverse problems of partial differential equations
[2] https://www.mathworks.com/help/deeplearning/ug/solve-partial-differential-equations-with-lbfgs-method-and-deep-learning.html

clear all;
close all;
clc;
%% Generate Training Data
% The first 25 is for the left/right boundary
numBoundaryConditionPoints = [128 128];
% This creates a row vector of 25 elements
x0BC1 = zeros(1,numBoundaryConditionPoints(1));
x0BC2 = ones(1,numBoundaryConditionPoints(2));
% This creates a vector of 25 equally spaced time points between 0 and 1.
t0BC1 = linspace(0,1,numBoundaryConditionPoints(1));
t0BC2 = linspace(0,1,numBoundaryConditionPoints(2));
% Calculate boundary
u0BC1 = 12*sech(-4*t0BC1).^2;
u0BC2 = 12*sech(1 – 4*t0BC2).^2;
numInitialConditionPoints = 256;
x0IC = linspace(0,1,numInitialConditionPoints);
t0IC = zeros(1,numInitialConditionPoints);
% Initial condition
u0IC = 12*sech(x0IC).^2;
% Group together the data for initial and boundary conditions.
X0 = [x0IC x0BC1 x0BC2];
T0 = [t0IC t0BC1 t0BC2];
U0 = [u0IC u0BC1 u0BC2];
% Defining the Number of Points
numInternalCollocationPoints = 10000;
% Generating Random Points in a Unit Square
points = rand(numInternalCollocationPoints,2);
dataX = 2*points(:,1);
dataT = points(:,2);
%% Define Neural Network Architecture
numBlocks = 8;
fcOutputSize = 20;
% This creates a fundamental block that will be repeated:
fcBlock = [
fullyConnectedLayer(fcOutputSize)
tanhLayer];
layers = [
featureInputLayer(2) % featureInputLayer(2): This is the input layer that accepts your features. The 2 corresponds to (x, t) coordinates.
repmat(fcBlock,[numBlocks 1]) % Creates a deep network: Input → Block 1 → Block 2 → … → Block N
fullyConnectedLayer(1)
];
% Convert the layer array to a dlnetwork object.
net = dlnetwork(layers);
% Training a PINN can result in better accuracy when the learnable parameters have data type double.
% Convert the network learnables to double using the dlupdate function.
% Note that not all neural networks support learnables of type double, for example, networks that use GPU optimizations that rely on learnables with type single.
net = dlupdate(@double,net);
%% Define Model Loss Function
% This is the core loss function that makes Physics-Informed Neural Networks (PINNs) work! It’s where the "physics" is enforced.
function [loss,gradients] = modelLoss(net,X,T,X0,T0,U0)
% Make predictions with the initial conditions.
XT = cat(1,X,T);
U = forward(net,XT);
% Calculate derivatives with respect to X and T.
X = stripdims(X);
T = stripdims(T);
U = stripdims(U);
Ux = dljacobian(U,X,1);
Ut = dljacobian(U,T,1);
% Calculate second-order derivatives with respect to X.
Uxx = dldivergence(Ux,X,1);
Uxxx = dldivergence(Uxx,X,1);
% Calculate mseF. (Physics Loss 1: The PDE)
f = Ut + U.*Ux + Uxxx;
mseF = mean(f.^2);

% Calculate mseG. (Physics Loss 2: Your new constraint)
g = 4.*Ux + Ut;% + (X.*U)./2;
mseG = mean(g.^2);
% Calculate mseU. (Data Loss: Initial + Boundary)
XT0 = cat(1,X0,T0);
U0Pred = forward(net,XT0);
mseU = l2loss(U0Pred,U0);
% Calculated loss
loss = mseF + mseU + mseG;
% Calculate gradients with respect to the learnable parameters.
gradients = dlgradient(loss,net.Learnables);
end
%% Specify the training options:
solverState = lbfgsState;
maxIterations = 500;
gradientTolerance = 1e-5;
stepTolerance = 1e-5;
%% Train Neural Network
% Convert the training data to dlarray objects.
% Specify that the inputs X and T have format "BC" (batch, channel) and that the initial conditions have format "CB" (channel, batch).
X = dlarray(dataX,"BC");
T = dlarray(dataT,"BC");
X0 = dlarray(X0,"CB");
T0 = dlarray(T0,"CB");
U0 = dlarray(U0,"CB");
% Accelerate the loss function using the dlaccelerate function.
accfun = dlaccelerate(@modelLoss);
% Create a function handle containing the loss function for the L-BFGS update step.
% In order to evaluate the dlgradient function inside the modelLoss function using automatic differentiation, use the dlfeval function.
lossFcn = @(net) dlfeval(accfun,net,X,T,X0,T0,U0);
% Initialize the TrainingProgressMonitor object.
% At each iteration, plot the loss and monitor the norm of the gradients and steps.
% Because the timer starts when you create the monitor object, make sure that you create the object close to the training loop.
monitor = trainingProgressMonitor( …
Metrics="TrainingLoss", …
Info=["Iteration" "GradientsNorm" "StepNorm"], …
XLabel="Iteration");
iteration = 0;
while iteration < maxIterations && ~monitor.Stop
iteration = iteration + 1;
[net, solverState] = lbfgsupdate(net,lossFcn,solverState);
updateInfo(monitor, …
Iteration=iteration, …
GradientsNorm=solverState.GradientsNorm, …
StepNorm=solverState.StepNorm);
recordMetrics(monitor,iteration,TrainingLoss=solverState.Loss);
monitor.Progress = 100*iteration/maxIterations;
if solverState.GradientsNorm < gradientTolerance || …
solverState.StepNorm < stepTolerance || …
solverState.LineSearchStatus == "failed"
break
end
end
%% Exact solution for your specific case
function U = solveEq(X,T)

U = 12*sech(X-4.*T).^2;
end
%% Evaluate Model Accuracy
tTest = [0.25 0.5 0.75 1];
numObservationsTest = numel(tTest);
szXTest = 1001;
XTest = linspace(0,1,szXTest);
XTest = dlarray(XTest,"CB");
% Test the model.
UPred = zeros(numObservationsTest,szXTest);
UTest = zeros(numObservationsTest,szXTest);
for i = 1:numObservationsTest
t = tTest(i);
TTest = repmat(t,[1 szXTest]);
TTest = dlarray(TTest,"CB");
XTTest = cat(1,XTest,TTest);
UPred(i,:) = forward(net,XTTest);
UTest(i,:) = solveEq(extractdata(XTest),t);
end
err = norm(UPred – UTest) / norm(UTest);
fprintf(‘Relative error: %en’, err);
figure
tiledlayout("flow")
for i = 1:numel(tTest)
nexttile

plot(XTest,UPred(i,:),"-",LineWidth=2);
hold on
plot(XTest, UTest(i,:),"–",LineWidth=2)
hold off
ylim([0, 13])
xlabel("x")
ylabel("u(x," + t + ")")
end
legend(["Prediction" "Target"])
%% Create Density Plots with Rainbow Color Range
% Create a finer grid for density plots
xGrid = linspace(0, 1, 200);
tGrid = linspace(0, 1, 100);
[XGrid, TGrid] = meshgrid(xGrid, tGrid);
% Create predicted solution matrix
UPredDensity = zeros(length(tGrid), length(xGrid));
UTestDensity = zeros(length(tGrid), length(xGrid));
% Generate predictions for each point in the grid
for i = 1:length(tGrid)
for j = 1:length(xGrid)
% Predicted solution
XPoint = dlarray(xGrid(j), "CB");
TPoint = dlarray(tGrid(i), "CB");
XTPoint = cat(1, XPoint, TPoint);
UPredDensity(i,j) = extractdata(forward(net, XTPoint));

% Exact solution
UTestDensity(i,j) = solveEq(XGrid(j), TGrid(i));
end
end
% Create density plots
figure(‘Position’, [100, 100, 1200, 500]);
% Predicted solution density plot
subplot(1,2,1);
imagesc(xGrid, tGrid, UPredDensity);
colormap(jet); % Rainbow colormap
colorbar;
axis xy; % Correct orientation (time increasing downward)
xlabel(‘x’);
ylabel(‘t’);
title(‘Predicted Solution Density’);
set(gca, ‘FontSize’, 12);
% Exact solution density plot
subplot(1,2,2);
imagesc(xGrid, tGrid, UTestDensity);
colormap(jet); % Rainbow colormap
colorbar;
axis xy; % Correct orientation (time increasing downward)
xlabel(‘x’);
ylabel(‘t’);
title(‘Exact Solution Density’);
set(gca, ‘FontSize’, 12);
% Add a main title
sgtitle(‘Solution Comparison – Density Plots’, ‘FontSize’, 14, ‘FontWeight’, ‘bold’);
%% Line plots for specific time points (your original visualization)
figure(‘Position’, [100, 100, 1000, 800]);
tiledlayout("flow")
for i = 1:numel(tTest)
nexttile

plot(XTest,UPred(i,:),"-",LineWidth=2);
hold on
plot(XTest, UTest(i,:),"–",LineWidth=2)
hold off
ylim([0, 13])
xlabel("x")
ylabel("u(x," + tTest(i) + ")")
title(sprintf(‘t = %.2f’, tTest(i)))
end
legend(["Prediction" "Target"])
sgtitle(‘Solution Comparison – Time Slices’, ‘FontSize’, 14, ‘FontWeight’, ‘bold’);Hi everyone, recently I started to work on PINN. I tried to apply Lie symmetries enhanced PINN (sPINN). For this purpose, I tried to train the Kdv equation in [1] with the same conditions. The problem is, in theory, sPINN must give a better approximation than classic PINN, but in my code, I think something is missing. I changed the initial condition, equation, and added the symmetry condition of the code in [2].
[1] Enforcing continuous symmetries in physics-informed neural network for solving forward and inverse problems of partial differential equations
[2] https://www.mathworks.com/help/deeplearning/ug/solve-partial-differential-equations-with-lbfgs-method-and-deep-learning.html

clear all;
close all;
clc;
%% Generate Training Data
% The first 25 is for the left/right boundary
numBoundaryConditionPoints = [128 128];
% This creates a row vector of 25 elements
x0BC1 = zeros(1,numBoundaryConditionPoints(1));
x0BC2 = ones(1,numBoundaryConditionPoints(2));
% This creates a vector of 25 equally spaced time points between 0 and 1.
t0BC1 = linspace(0,1,numBoundaryConditionPoints(1));
t0BC2 = linspace(0,1,numBoundaryConditionPoints(2));
% Calculate boundary
u0BC1 = 12*sech(-4*t0BC1).^2;
u0BC2 = 12*sech(1 – 4*t0BC2).^2;
numInitialConditionPoints = 256;
x0IC = linspace(0,1,numInitialConditionPoints);
t0IC = zeros(1,numInitialConditionPoints);
% Initial condition
u0IC = 12*sech(x0IC).^2;
% Group together the data for initial and boundary conditions.
X0 = [x0IC x0BC1 x0BC2];
T0 = [t0IC t0BC1 t0BC2];
U0 = [u0IC u0BC1 u0BC2];
% Defining the Number of Points
numInternalCollocationPoints = 10000;
% Generating Random Points in a Unit Square
points = rand(numInternalCollocationPoints,2);
dataX = 2*points(:,1);
dataT = points(:,2);
%% Define Neural Network Architecture
numBlocks = 8;
fcOutputSize = 20;
% This creates a fundamental block that will be repeated:
fcBlock = [
fullyConnectedLayer(fcOutputSize)
tanhLayer];
layers = [
featureInputLayer(2) % featureInputLayer(2): This is the input layer that accepts your features. The 2 corresponds to (x, t) coordinates.
repmat(fcBlock,[numBlocks 1]) % Creates a deep network: Input → Block 1 → Block 2 → … → Block N
fullyConnectedLayer(1)
];
% Convert the layer array to a dlnetwork object.
net = dlnetwork(layers);
% Training a PINN can result in better accuracy when the learnable parameters have data type double.
% Convert the network learnables to double using the dlupdate function.
% Note that not all neural networks support learnables of type double, for example, networks that use GPU optimizations that rely on learnables with type single.
net = dlupdate(@double,net);
%% Define Model Loss Function
% This is the core loss function that makes Physics-Informed Neural Networks (PINNs) work! It’s where the "physics" is enforced.
function [loss,gradients] = modelLoss(net,X,T,X0,T0,U0)
% Make predictions with the initial conditions.
XT = cat(1,X,T);
U = forward(net,XT);
% Calculate derivatives with respect to X and T.
X = stripdims(X);
T = stripdims(T);
U = stripdims(U);
Ux = dljacobian(U,X,1);
Ut = dljacobian(U,T,1);
% Calculate second-order derivatives with respect to X.
Uxx = dldivergence(Ux,X,1);
Uxxx = dldivergence(Uxx,X,1);
% Calculate mseF. (Physics Loss 1: The PDE)
f = Ut + U.*Ux + Uxxx;
mseF = mean(f.^2);

% Calculate mseG. (Physics Loss 2: Your new constraint)
g = 4.*Ux + Ut;% + (X.*U)./2;
mseG = mean(g.^2);
% Calculate mseU. (Data Loss: Initial + Boundary)
XT0 = cat(1,X0,T0);
U0Pred = forward(net,XT0);
mseU = l2loss(U0Pred,U0);
% Calculated loss
loss = mseF + mseU + mseG;
% Calculate gradients with respect to the learnable parameters.
gradients = dlgradient(loss,net.Learnables);
end
%% Specify the training options:
solverState = lbfgsState;
maxIterations = 500;
gradientTolerance = 1e-5;
stepTolerance = 1e-5;
%% Train Neural Network
% Convert the training data to dlarray objects.
% Specify that the inputs X and T have format "BC" (batch, channel) and that the initial conditions have format "CB" (channel, batch).
X = dlarray(dataX,"BC");
T = dlarray(dataT,"BC");
X0 = dlarray(X0,"CB");
T0 = dlarray(T0,"CB");
U0 = dlarray(U0,"CB");
% Accelerate the loss function using the dlaccelerate function.
accfun = dlaccelerate(@modelLoss);
% Create a function handle containing the loss function for the L-BFGS update step.
% In order to evaluate the dlgradient function inside the modelLoss function using automatic differentiation, use the dlfeval function.
lossFcn = @(net) dlfeval(accfun,net,X,T,X0,T0,U0);
% Initialize the TrainingProgressMonitor object.
% At each iteration, plot the loss and monitor the norm of the gradients and steps.
% Because the timer starts when you create the monitor object, make sure that you create the object close to the training loop.
monitor = trainingProgressMonitor( …
Metrics="TrainingLoss", …
Info=["Iteration" "GradientsNorm" "StepNorm"], …
XLabel="Iteration");
iteration = 0;
while iteration < maxIterations && ~monitor.Stop
iteration = iteration + 1;
[net, solverState] = lbfgsupdate(net,lossFcn,solverState);
updateInfo(monitor, …
Iteration=iteration, …
GradientsNorm=solverState.GradientsNorm, …
StepNorm=solverState.StepNorm);
recordMetrics(monitor,iteration,TrainingLoss=solverState.Loss);
monitor.Progress = 100*iteration/maxIterations;
if solverState.GradientsNorm < gradientTolerance || …
solverState.StepNorm < stepTolerance || …
solverState.LineSearchStatus == "failed"
break
end
end
%% Exact solution for your specific case
function U = solveEq(X,T)

U = 12*sech(X-4.*T).^2;
end
%% Evaluate Model Accuracy
tTest = [0.25 0.5 0.75 1];
numObservationsTest = numel(tTest);
szXTest = 1001;
XTest = linspace(0,1,szXTest);
XTest = dlarray(XTest,"CB");
% Test the model.
UPred = zeros(numObservationsTest,szXTest);
UTest = zeros(numObservationsTest,szXTest);
for i = 1:numObservationsTest
t = tTest(i);
TTest = repmat(t,[1 szXTest]);
TTest = dlarray(TTest,"CB");
XTTest = cat(1,XTest,TTest);
UPred(i,:) = forward(net,XTTest);
UTest(i,:) = solveEq(extractdata(XTest),t);
end
err = norm(UPred – UTest) / norm(UTest);
fprintf(‘Relative error: %en’, err);
figure
tiledlayout("flow")
for i = 1:numel(tTest)
nexttile

plot(XTest,UPred(i,:),"-",LineWidth=2);
hold on
plot(XTest, UTest(i,:),"–",LineWidth=2)
hold off
ylim([0, 13])
xlabel("x")
ylabel("u(x," + t + ")")
end
legend(["Prediction" "Target"])
%% Create Density Plots with Rainbow Color Range
% Create a finer grid for density plots
xGrid = linspace(0, 1, 200);
tGrid = linspace(0, 1, 100);
[XGrid, TGrid] = meshgrid(xGrid, tGrid);
% Create predicted solution matrix
UPredDensity = zeros(length(tGrid), length(xGrid));
UTestDensity = zeros(length(tGrid), length(xGrid));
% Generate predictions for each point in the grid
for i = 1:length(tGrid)
for j = 1:length(xGrid)
% Predicted solution
XPoint = dlarray(xGrid(j), "CB");
TPoint = dlarray(tGrid(i), "CB");
XTPoint = cat(1, XPoint, TPoint);
UPredDensity(i,j) = extractdata(forward(net, XTPoint));

% Exact solution
UTestDensity(i,j) = solveEq(XGrid(j), TGrid(i));
end
end
% Create density plots
figure(‘Position’, [100, 100, 1200, 500]);
% Predicted solution density plot
subplot(1,2,1);
imagesc(xGrid, tGrid, UPredDensity);
colormap(jet); % Rainbow colormap
colorbar;
axis xy; % Correct orientation (time increasing downward)
xlabel(‘x’);
ylabel(‘t’);
title(‘Predicted Solution Density’);
set(gca, ‘FontSize’, 12);
% Exact solution density plot
subplot(1,2,2);
imagesc(xGrid, tGrid, UTestDensity);
colormap(jet); % Rainbow colormap
colorbar;
axis xy; % Correct orientation (time increasing downward)
xlabel(‘x’);
ylabel(‘t’);
title(‘Exact Solution Density’);
set(gca, ‘FontSize’, 12);
% Add a main title
sgtitle(‘Solution Comparison – Density Plots’, ‘FontSize’, 14, ‘FontWeight’, ‘bold’);
%% Line plots for specific time points (your original visualization)
figure(‘Position’, [100, 100, 1000, 800]);
tiledlayout("flow")
for i = 1:numel(tTest)
nexttile

plot(XTest,UPred(i,:),"-",LineWidth=2);
hold on
plot(XTest, UTest(i,:),"–",LineWidth=2)
hold off
ylim([0, 13])
xlabel("x")
ylabel("u(x," + tTest(i) + ")")
title(sprintf(‘t = %.2f’, tTest(i)))
end
legend(["Prediction" "Target"])
sgtitle(‘Solution Comparison – Time Slices’, ‘FontSize’, 14, ‘FontWeight’, ‘bold’); Hi everyone, recently I started to work on PINN. I tried to apply Lie symmetries enhanced PINN (sPINN). For this purpose, I tried to train the Kdv equation in [1] with the same conditions. The problem is, in theory, sPINN must give a better approximation than classic PINN, but in my code, I think something is missing. I changed the initial condition, equation, and added the symmetry condition of the code in [2].
[1] Enforcing continuous symmetries in physics-informed neural network for solving forward and inverse problems of partial differential equations
[2] https://www.mathworks.com/help/deeplearning/ug/solve-partial-differential-equations-with-lbfgs-method-and-deep-learning.html

clear all;
close all;
clc;
%% Generate Training Data
% The first 25 is for the left/right boundary
numBoundaryConditionPoints = [128 128];
% This creates a row vector of 25 elements
x0BC1 = zeros(1,numBoundaryConditionPoints(1));
x0BC2 = ones(1,numBoundaryConditionPoints(2));
% This creates a vector of 25 equally spaced time points between 0 and 1.
t0BC1 = linspace(0,1,numBoundaryConditionPoints(1));
t0BC2 = linspace(0,1,numBoundaryConditionPoints(2));
% Calculate boundary
u0BC1 = 12*sech(-4*t0BC1).^2;
u0BC2 = 12*sech(1 – 4*t0BC2).^2;
numInitialConditionPoints = 256;
x0IC = linspace(0,1,numInitialConditionPoints);
t0IC = zeros(1,numInitialConditionPoints);
% Initial condition
u0IC = 12*sech(x0IC).^2;
% Group together the data for initial and boundary conditions.
X0 = [x0IC x0BC1 x0BC2];
T0 = [t0IC t0BC1 t0BC2];
U0 = [u0IC u0BC1 u0BC2];
% Defining the Number of Points
numInternalCollocationPoints = 10000;
% Generating Random Points in a Unit Square
points = rand(numInternalCollocationPoints,2);
dataX = 2*points(:,1);
dataT = points(:,2);
%% Define Neural Network Architecture
numBlocks = 8;
fcOutputSize = 20;
% This creates a fundamental block that will be repeated:
fcBlock = [
fullyConnectedLayer(fcOutputSize)
tanhLayer];
layers = [
featureInputLayer(2) % featureInputLayer(2): This is the input layer that accepts your features. The 2 corresponds to (x, t) coordinates.
repmat(fcBlock,[numBlocks 1]) % Creates a deep network: Input → Block 1 → Block 2 → … → Block N
fullyConnectedLayer(1)
];
% Convert the layer array to a dlnetwork object.
net = dlnetwork(layers);
% Training a PINN can result in better accuracy when the learnable parameters have data type double.
% Convert the network learnables to double using the dlupdate function.
% Note that not all neural networks support learnables of type double, for example, networks that use GPU optimizations that rely on learnables with type single.
net = dlupdate(@double,net);
%% Define Model Loss Function
% This is the core loss function that makes Physics-Informed Neural Networks (PINNs) work! It’s where the "physics" is enforced.
function [loss,gradients] = modelLoss(net,X,T,X0,T0,U0)
% Make predictions with the initial conditions.
XT = cat(1,X,T);
U = forward(net,XT);
% Calculate derivatives with respect to X and T.
X = stripdims(X);
T = stripdims(T);
U = stripdims(U);
Ux = dljacobian(U,X,1);
Ut = dljacobian(U,T,1);
% Calculate second-order derivatives with respect to X.
Uxx = dldivergence(Ux,X,1);
Uxxx = dldivergence(Uxx,X,1);
% Calculate mseF. (Physics Loss 1: The PDE)
f = Ut + U.*Ux + Uxxx;
mseF = mean(f.^2);

% Calculate mseG. (Physics Loss 2: Your new constraint)
g = 4.*Ux + Ut;% + (X.*U)./2;
mseG = mean(g.^2);
% Calculate mseU. (Data Loss: Initial + Boundary)
XT0 = cat(1,X0,T0);
U0Pred = forward(net,XT0);
mseU = l2loss(U0Pred,U0);
% Calculated loss
loss = mseF + mseU + mseG;
% Calculate gradients with respect to the learnable parameters.
gradients = dlgradient(loss,net.Learnables);
end
%% Specify the training options:
solverState = lbfgsState;
maxIterations = 500;
gradientTolerance = 1e-5;
stepTolerance = 1e-5;
%% Train Neural Network
% Convert the training data to dlarray objects.
% Specify that the inputs X and T have format "BC" (batch, channel) and that the initial conditions have format "CB" (channel, batch).
X = dlarray(dataX,"BC");
T = dlarray(dataT,"BC");
X0 = dlarray(X0,"CB");
T0 = dlarray(T0,"CB");
U0 = dlarray(U0,"CB");
% Accelerate the loss function using the dlaccelerate function.
accfun = dlaccelerate(@modelLoss);
% Create a function handle containing the loss function for the L-BFGS update step.
% In order to evaluate the dlgradient function inside the modelLoss function using automatic differentiation, use the dlfeval function.
lossFcn = @(net) dlfeval(accfun,net,X,T,X0,T0,U0);
% Initialize the TrainingProgressMonitor object.
% At each iteration, plot the loss and monitor the norm of the gradients and steps.
% Because the timer starts when you create the monitor object, make sure that you create the object close to the training loop.
monitor = trainingProgressMonitor( …
Metrics="TrainingLoss", …
Info=["Iteration" "GradientsNorm" "StepNorm"], …
XLabel="Iteration");
iteration = 0;
while iteration < maxIterations && ~monitor.Stop
iteration = iteration + 1;
[net, solverState] = lbfgsupdate(net,lossFcn,solverState);
updateInfo(monitor, …
Iteration=iteration, …
GradientsNorm=solverState.GradientsNorm, …
StepNorm=solverState.StepNorm);
recordMetrics(monitor,iteration,TrainingLoss=solverState.Loss);
monitor.Progress = 100*iteration/maxIterations;
if solverState.GradientsNorm < gradientTolerance || …
solverState.StepNorm < stepTolerance || …
solverState.LineSearchStatus == "failed"
break
end
end
%% Exact solution for your specific case
function U = solveEq(X,T)

U = 12*sech(X-4.*T).^2;
end
%% Evaluate Model Accuracy
tTest = [0.25 0.5 0.75 1];
numObservationsTest = numel(tTest);
szXTest = 1001;
XTest = linspace(0,1,szXTest);
XTest = dlarray(XTest,"CB");
% Test the model.
UPred = zeros(numObservationsTest,szXTest);
UTest = zeros(numObservationsTest,szXTest);
for i = 1:numObservationsTest
t = tTest(i);
TTest = repmat(t,[1 szXTest]);
TTest = dlarray(TTest,"CB");
XTTest = cat(1,XTest,TTest);
UPred(i,:) = forward(net,XTTest);
UTest(i,:) = solveEq(extractdata(XTest),t);
end
err = norm(UPred – UTest) / norm(UTest);
fprintf(‘Relative error: %en’, err);
figure
tiledlayout("flow")
for i = 1:numel(tTest)
nexttile

plot(XTest,UPred(i,:),"-",LineWidth=2);
hold on
plot(XTest, UTest(i,:),"–",LineWidth=2)
hold off
ylim([0, 13])
xlabel("x")
ylabel("u(x," + t + ")")
end
legend(["Prediction" "Target"])
%% Create Density Plots with Rainbow Color Range
% Create a finer grid for density plots
xGrid = linspace(0, 1, 200);
tGrid = linspace(0, 1, 100);
[XGrid, TGrid] = meshgrid(xGrid, tGrid);
% Create predicted solution matrix
UPredDensity = zeros(length(tGrid), length(xGrid));
UTestDensity = zeros(length(tGrid), length(xGrid));
% Generate predictions for each point in the grid
for i = 1:length(tGrid)
for j = 1:length(xGrid)
% Predicted solution
XPoint = dlarray(xGrid(j), "CB");
TPoint = dlarray(tGrid(i), "CB");
XTPoint = cat(1, XPoint, TPoint);
UPredDensity(i,j) = extractdata(forward(net, XTPoint));

% Exact solution
UTestDensity(i,j) = solveEq(XGrid(j), TGrid(i));
end
end
% Create density plots
figure(‘Position’, [100, 100, 1200, 500]);
% Predicted solution density plot
subplot(1,2,1);
imagesc(xGrid, tGrid, UPredDensity);
colormap(jet); % Rainbow colormap
colorbar;
axis xy; % Correct orientation (time increasing downward)
xlabel(‘x’);
ylabel(‘t’);
title(‘Predicted Solution Density’);
set(gca, ‘FontSize’, 12);
% Exact solution density plot
subplot(1,2,2);
imagesc(xGrid, tGrid, UTestDensity);
colormap(jet); % Rainbow colormap
colorbar;
axis xy; % Correct orientation (time increasing downward)
xlabel(‘x’);
ylabel(‘t’);
title(‘Exact Solution Density’);
set(gca, ‘FontSize’, 12);
% Add a main title
sgtitle(‘Solution Comparison – Density Plots’, ‘FontSize’, 14, ‘FontWeight’, ‘bold’);
%% Line plots for specific time points (your original visualization)
figure(‘Position’, [100, 100, 1000, 800]);
tiledlayout("flow")
for i = 1:numel(tTest)
nexttile

plot(XTest,UPred(i,:),"-",LineWidth=2);
hold on
plot(XTest, UTest(i,:),"–",LineWidth=2)
hold off
ylim([0, 13])
xlabel("x")
ylabel("u(x," + tTest(i) + ")")
title(sprintf(‘t = %.2f’, tTest(i)))
end
legend(["Prediction" "Target"])
sgtitle(‘Solution Comparison – Time Slices’, ‘FontSize’, 14, ‘FontWeight’, ‘bold’); pinn, deep learning, neural network, neural networks, pde, physics-informed neural network MATLAB Answers — New Questions

​

Given a filter vH I’m looking for vectors vR and vC such that:
toeplitz(vC, vR) * vX = conv(vX, vH, ‘same’);
For instance, for vH = [1, 2, 3, 4] and length(vX) = 7; the matrix is given by:
mH =

3 2 1 0 0 0 0
4 3 2 1 0 0 0
0 4 3 2 1 0 0
0 0 4 3 2 1 0
0 0 0 4 3 2 1
0 0 0 0 4 3 2
0 0 0 0 0 4 3Given a filter vH I’m looking for vectors vR and vC such that:
toeplitz(vC, vR) * vX = conv(vX, vH, ‘same’);
For instance, for vH = [1, 2, 3, 4] and length(vX) = 7; the matrix is given by:
mH =

3 2 1 0 0 0 0
4 3 2 1 0 0 0
0 4 3 2 1 0 0
0 0 4 3 2 1 0
0 0 0 4 3 2 1
0 0 0 0 4 3 2
0 0 0 0 0 4 3 Given a filter vH I’m looking for vectors vR and vC such that:
toeplitz(vC, vR) * vX = conv(vX, vH, ‘same’);
For instance, for vH = [1, 2, 3, 4] and length(vX) = 7; the matrix is given by:
mH =

3 2 1 0 0 0 0
4 3 2 1 0 0 0
0 4 3 2 1 0 0
0 0 4 3 2 1 0
0 0 0 4 3 2 1
0 0 0 0 4 3 2
0 0 0 0 0 4 3 convolution, matrix, toeplitz, convolution-matrix MATLAB Answers — New Questions

​

I am trying to take some random noise (produced by a different script), Fourier transform it, multiply it by a filter, and then do an inverse Fourier transform to get some random noise data back. When I was testing my script with a filter which has a value of 1 for all frequencies (i.e. should give back the original data after IFFT), I realized all of the resulting values are shifted by 1 element. I.e., if I plot the original vs multiplied (‘calibrated’) noise it looks like this:

but then if I just circshift one of the arrays, either the noise given or the post-FT noise, by 1 (in opposite directions), it looks like this:

(and the values of the two arrays are equal to within 1e-15 tolerance, which is good enough for my purpose). I suspect the problem is how I’m setting up my frequency arrays/interpolating my actual function I need to multiply by, but I’m pretty much stuck after that–any suggestions would be appreciated.

More in-depth info
Full script is attached (spaghetti code beware, apologies in advance), but it has a lot of plots/troubleshooting, so here is the relevant code:

%%read files
[tempFile, tempPath] = uigetfile(‘*.csv’, ‘Select the calibration data file’);
calData = readmatrix(fullfile(tempPath, tempFile));
[tempFile2, tempPath2] = uigetfile(‘*.txt’, ‘Select the random noise’);
randNoise = readmatrix(fullfile(tempPath2, tempFile2));

%% Sort and format calibration daya

%sort calibration data by period
clDatSorted=sortrows(calData,[1]);

%extract data
periods = clDatSorted(:,1);
ampsRequired = clDatSorted(:,2);

%mirror the function in the negative frequency domain due to the nature of
%the FT function
ampsRequired = [flip(ampsRequired);ampsRequired];
periods = [flip(periods)*-1;periods];

freqs = 1./periods;

%% Fourier transform the random noise and plot

fourierNoise = fft(randNoise);
fourierNoise = fftshift(fourierNoise); %fftshift used here to center zero-frequency value

Ts = inputdlg(‘What is the sample period?’); %sample period; user defined because of the way the script to generate my noise is set up
Ts=str2num(Ts{1}); %convert to a number

f= ((-length(fourierNoise)/2):((length(fourierNoise)/2)-1))*fs/length(fourierNoise);

%% interpolate calibration function
%this is going to be important because my calibration function is manually
%obtained so I will need to extrapolate *and* interpolate, unfortunately–I
%can’t just give it a smooth function due to the nature of the data

interpolatedCal=interp1(freqs(2:end-1),ampsRequired(2:end-1),f,’linear’,’extrap’);

%% calibrate

calibratedFourierNoise = interpolatedCal .* fourierNoise’;
calibratedNoise = ifft(ifftshift(calibratedFourierNoise));

if size(calibratedNoise)~=size(randNoise)
calibratedNoise = flip(calibratedNoise); %to fix row-column swaps–I know this needs a better fix
end

And
ismembertol(circshift(randNoise,[0, 1]),calibratedNoise,1e-15)
produces 1’s everywhere.
I think the line where I define my frequency:
f= ((-length(fourierNoise)/2):((length(fourierNoise)/2)-1))*fs/length(fourierNoise);
is the root of the problem but I’ve tried playing around with it and keep encountering the same issue.
In particular, if I do
[p,fp] = pspectrum(randNoise);
the maximum frequency it gives me is 3.14 for this data, and I’m assuming that the max frequency for the Fourier transform is 1/2 the number of random noise values per second–I feel like this is an issue with my lack of deep understanding of Fourier theory tbh, but I can’t pinpoint the exact issue.

Full script/test calibration file with ones everywhere (i.e. flat filter)/sample noise/sample calibration (with ones everywhere as used for the test in sampleCalOneEverywhere and as the filter I’ll aactually be using in sampleCal1) are attached.

(Not super relevant but the final filter will be an empirically-obtained low-pass filter with some added stuff.)I am trying to take some random noise (produced by a different script), Fourier transform it, multiply it by a filter, and then do an inverse Fourier transform to get some random noise data back. When I was testing my script with a filter which has a value of 1 for all frequencies (i.e. should give back the original data after IFFT), I realized all of the resulting values are shifted by 1 element. I.e., if I plot the original vs multiplied (‘calibrated’) noise it looks like this:

but then if I just circshift one of the arrays, either the noise given or the post-FT noise, by 1 (in opposite directions), it looks like this:

(and the values of the two arrays are equal to within 1e-15 tolerance, which is good enough for my purpose). I suspect the problem is how I’m setting up my frequency arrays/interpolating my actual function I need to multiply by, but I’m pretty much stuck after that–any suggestions would be appreciated.

More in-depth info
Full script is attached (spaghetti code beware, apologies in advance), but it has a lot of plots/troubleshooting, so here is the relevant code:

%%read files
[tempFile, tempPath] = uigetfile(‘*.csv’, ‘Select the calibration data file’);
calData = readmatrix(fullfile(tempPath, tempFile));
[tempFile2, tempPath2] = uigetfile(‘*.txt’, ‘Select the random noise’);
randNoise = readmatrix(fullfile(tempPath2, tempFile2));

%% Sort and format calibration daya

%sort calibration data by period
clDatSorted=sortrows(calData,[1]);

%extract data
periods = clDatSorted(:,1);
ampsRequired = clDatSorted(:,2);

%mirror the function in the negative frequency domain due to the nature of
%the FT function
ampsRequired = [flip(ampsRequired);ampsRequired];
periods = [flip(periods)*-1;periods];

freqs = 1./periods;

%% Fourier transform the random noise and plot

fourierNoise = fft(randNoise);
fourierNoise = fftshift(fourierNoise); %fftshift used here to center zero-frequency value

Ts = inputdlg(‘What is the sample period?’); %sample period; user defined because of the way the script to generate my noise is set up
Ts=str2num(Ts{1}); %convert to a number

f= ((-length(fourierNoise)/2):((length(fourierNoise)/2)-1))*fs/length(fourierNoise);

%% interpolate calibration function
%this is going to be important because my calibration function is manually
%obtained so I will need to extrapolate *and* interpolate, unfortunately–I
%can’t just give it a smooth function due to the nature of the data

interpolatedCal=interp1(freqs(2:end-1),ampsRequired(2:end-1),f,’linear’,’extrap’);

%% calibrate

calibratedFourierNoise = interpolatedCal .* fourierNoise’;
calibratedNoise = ifft(ifftshift(calibratedFourierNoise));

if size(calibratedNoise)~=size(randNoise)
calibratedNoise = flip(calibratedNoise); %to fix row-column swaps–I know this needs a better fix
end

And
ismembertol(circshift(randNoise,[0, 1]),calibratedNoise,1e-15)
produces 1’s everywhere.
I think the line where I define my frequency:
f= ((-length(fourierNoise)/2):((length(fourierNoise)/2)-1))*fs/length(fourierNoise);
is the root of the problem but I’ve tried playing around with it and keep encountering the same issue.
In particular, if I do
[p,fp] = pspectrum(randNoise);
the maximum frequency it gives me is 3.14 for this data, and I’m assuming that the max frequency for the Fourier transform is 1/2 the number of random noise values per second–I feel like this is an issue with my lack of deep understanding of Fourier theory tbh, but I can’t pinpoint the exact issue.

Full script/test calibration file with ones everywhere (i.e. flat filter)/sample noise/sample calibration (with ones everywhere as used for the test in sampleCalOneEverywhere and as the filter I’ll aactually be using in sampleCal1) are attached.

(Not super relevant but the final filter will be an empirically-obtained low-pass filter with some added stuff.) I am trying to take some random noise (produced by a different script), Fourier transform it, multiply it by a filter, and then do an inverse Fourier transform to get some random noise data back. When I was testing my script with a filter which has a value of 1 for all frequencies (i.e. should give back the original data after IFFT), I realized all of the resulting values are shifted by 1 element. I.e., if I plot the original vs multiplied (‘calibrated’) noise it looks like this:

but then if I just circshift one of the arrays, either the noise given or the post-FT noise, by 1 (in opposite directions), it looks like this:

(and the values of the two arrays are equal to within 1e-15 tolerance, which is good enough for my purpose). I suspect the problem is how I’m setting up my frequency arrays/interpolating my actual function I need to multiply by, but I’m pretty much stuck after that–any suggestions would be appreciated.

More in-depth info
Full script is attached (spaghetti code beware, apologies in advance), but it has a lot of plots/troubleshooting, so here is the relevant code:

%%read files
[tempFile, tempPath] = uigetfile(‘*.csv’, ‘Select the calibration data file’);
calData = readmatrix(fullfile(tempPath, tempFile));
[tempFile2, tempPath2] = uigetfile(‘*.txt’, ‘Select the random noise’);
randNoise = readmatrix(fullfile(tempPath2, tempFile2));

%% Sort and format calibration daya

%sort calibration data by period
clDatSorted=sortrows(calData,[1]);

%extract data
periods = clDatSorted(:,1);
ampsRequired = clDatSorted(:,2);

%mirror the function in the negative frequency domain due to the nature of
%the FT function
ampsRequired = [flip(ampsRequired);ampsRequired];
periods = [flip(periods)*-1;periods];

freqs = 1./periods;

%% Fourier transform the random noise and plot

fourierNoise = fft(randNoise);
fourierNoise = fftshift(fourierNoise); %fftshift used here to center zero-frequency value

Ts = inputdlg(‘What is the sample period?’); %sample period; user defined because of the way the script to generate my noise is set up
Ts=str2num(Ts{1}); %convert to a number

f= ((-length(fourierNoise)/2):((length(fourierNoise)/2)-1))*fs/length(fourierNoise);

%% interpolate calibration function
%this is going to be important because my calibration function is manually
%obtained so I will need to extrapolate *and* interpolate, unfortunately–I
%can’t just give it a smooth function due to the nature of the data

interpolatedCal=interp1(freqs(2:end-1),ampsRequired(2:end-1),f,’linear’,’extrap’);

%% calibrate

calibratedFourierNoise = interpolatedCal .* fourierNoise’;
calibratedNoise = ifft(ifftshift(calibratedFourierNoise));

if size(calibratedNoise)~=size(randNoise)
calibratedNoise = flip(calibratedNoise); %to fix row-column swaps–I know this needs a better fix
end

And
ismembertol(circshift(randNoise,[0, 1]),calibratedNoise,1e-15)
produces 1’s everywhere.
I think the line where I define my frequency:
f= ((-length(fourierNoise)/2):((length(fourierNoise)/2)-1))*fs/length(fourierNoise);
is the root of the problem but I’ve tried playing around with it and keep encountering the same issue.
In particular, if I do
[p,fp] = pspectrum(randNoise);
the maximum frequency it gives me is 3.14 for this data, and I’m assuming that the max frequency for the Fourier transform is 1/2 the number of random noise values per second–I feel like this is an issue with my lack of deep understanding of Fourier theory tbh, but I can’t pinpoint the exact issue.

Full script/test calibration file with ones everywhere (i.e. flat filter)/sample noise/sample calibration (with ones everywhere as used for the test in sampleCalOneEverywhere and as the filter I’ll aactually be using in sampleCal1) are attached.

(Not super relevant but the final filter will be an empirically-obtained low-pass filter with some added stuff.) fft, ifft, fourier transforms MATLAB Answers — New Questions

​ some manipulation -> IFFT results in one-element shift” />

Is there anybody who is actively using latest version 2025 Maple toolbox (as a part of Maple) with MATLAB R2025b? I am not able to install the Maple toolbox on MATLAB R2025b on Linux (installation process hangs).
I need to use the Maple toolbox for complicated symbolic computing which is not possible to perform via MATLAB symbolic toolbox (many symbolic matrix exponentials of 6×6 symbolic matrices, which takes on Matlab symbolic toolbox enormous CPU time).Is there anybody who is actively using latest version 2025 Maple toolbox (as a part of Maple) with MATLAB R2025b? I am not able to install the Maple toolbox on MATLAB R2025b on Linux (installation process hangs).
I need to use the Maple toolbox for complicated symbolic computing which is not possible to perform via MATLAB symbolic toolbox (many symbolic matrix exponentials of 6×6 symbolic matrices, which takes on Matlab symbolic toolbox enormous CPU time). Is there anybody who is actively using latest version 2025 Maple toolbox (as a part of Maple) with MATLAB R2025b? I am not able to install the Maple toolbox on MATLAB R2025b on Linux (installation process hangs).
I need to use the Maple toolbox for complicated symbolic computing which is not possible to perform via MATLAB symbolic toolbox (many symbolic matrix exponentials of 6×6 symbolic matrices, which takes on Matlab symbolic toolbox enormous CPU time). maple MATLAB Answers — New Questions

​