Adding supporting code for blog post

phiml-blog-supporting-code/FNO/fourierLayer.m

@@ -1,8 +1,8 @@
-function layer = fourierLayer(tWidth,numModes,args)
+function layer = fourierLayer(numModes,tWidth,args)
 
 arguments
-    tWidth
     numModes
+    tWidth
     args.Name = ""
 end
 name = args.Name;
@@ -11,7 +11,7 @@
 
 layers = [
     identityLayer(Name="in")
-    spectralConvolution1dLayer(tWidth,numModes,Name="specConv")
+    spectralConvolution1dLayer(numModes,tWidth,Name="specConv")
     additionLayer(2,Name="add")];
 
 net = addLayers(net,layers);

phiml-blog-supporting-code/FNO/spectralConvolution1dLayer.m

@@ -14,7 +14,7 @@
     end
 
     methods
-        function this = spectralConvolution1dLayer(outChannels,numModes,args)
+        function this = spectralConvolution1dLayer(numModes,outChannels,args)
             % spectralConvolution1dLayer   1-D Spectral Convolution Layer
             %
             %   layer = spectralConvolution1dLayer(outChannels, numModes)
@@ -34,8 +34,8 @@
             %                 default value is [].
 
             arguments
-                outChannels (1,1) double
                 numModes    (1,1) double
+                outChannels (1,1) double
                 args.Name {mustBeTextScalar} = "spectralConv1d"
                 args.Weights = []
             end

phiml-blog-supporting-code/PINN/solveNonlinearPendulum.m

@@ -1,7 +1,9 @@
 function sol = solveNonlinearPendulum(tspan,omega0,thetaDot0)
-    F = ode;
-    F.ODEFcn = @(t,x) [x(2); -omega0^2.*sin(x(1))];
-    F.InitialValue = [0; thetaDot0];
-    F.Solver = "ode45";
-    sol = solve(F,tspan);
+
+F = ode;
+F.ODEFcn = @(t,x) [x(2); -omega0^2.*sin(x(1))];
+F.InitialValue = [0; thetaDot0];
+F.Solver = "ode45";
+sol = solve(F,tspan);
+
 end

phiml-blog-supporting-code/README.md

@@ -1,13 +1,13 @@
 # Physics Informed Machine Learning Methods and Implementation supporting code
-This repository provides examples demonstrating a variety of Physics-Informed Machine Learning (PhiML) techniques, applied to a simple pendulum system. The examples provided here are discussed in detail in the accompanying blog post "Physics-Informed Machine Learning: Methods and Implementation". 
+This collection provides examples demonstrating a variety of Physics-Informed Machine Learning (PhiML) techniques, applied to a simple pendulum system. The examples provided here are discussed in detail in the accompanying blog post "Physics-Informed Machine Learning: Methods and Implementation". 
 
 ![hippo](https://www.mathworks.com/help/examples/symbolic/win64/SimulateThePhysicsOfAPendulumsPeriodicSwingExample_10.gif)
 
 The techniques described for the pendulum are categorized by their primary objectives:
 - **Modeling complex systems from data** 
     1. **Neural Ordinary Differential Equation**: learns underlying dynamics $f$ in the differential equation $\frac{d \mathbf{x}}{d t} = f(\mathbf{x},\mathbf{u})$ using a neural network.
     2. **Neural State-Space**: learns both the system dynamics $f$ and the measurement function $g$ in the state-space model $\frac{d \mathbf{x}}{dt} = f(\mathbf{x},\mathbf{u}), \mathbf{y}=g(\mathbf{x},\mathbf{u})$ using neural networks. Not shown in this repository, but illustrated in the documentation example [Neural State-Space Model of Simple Pendulum System](https://www.mathworks.com/help/ident/ug/training-a-neural-state-space-model-for-a-simple-pendulum-system.html). 
-    3. **Universal Differential Equation**: combines known dynamics $g$ with unknown dynamics $h$, e.g. $\frac{d\mathbf{x}}{dt} = f(\mathbf{x},\mathbf{u}) = g(\mathbf{x},\mathbf{u}) + h(\mathbf{x},\mathbf{u})$, learning the unknown part using a neural network. 
+    3. **Universal Differential Equation**: combines known dynamics $g$ with unknown dynamics $h$, for example $\frac{d\mathbf{x}}{dt} = f(\mathbf{x},\mathbf{u}) = g(\mathbf{x},\mathbf{u}) + h(\mathbf{x},\mathbf{u})$, learning the unknown part $h$ using a neural network. 
     4. **Hamiltonian Neural Network**: learns the system's Hamiltonian $\mathcal{H}$, and accounts for energy conservation by enforcing Hamilton's equations $\frac{dq}{dt} = \frac{\partial \mathcal{H}}{\partial p}, \frac{dp}{dt} = -\frac{\partial \mathcal{H}}{\partial q}$.
 - **Discovering governing equations from data:** 
     1. **SINDy (Sparse Identification of Nonlinear Dynamics)**: learns a mathematical representation of the system dynamics $f$ by performing sparse regression on a library of candidate functions.