Machine Learning informato dalla fisica

Estendere i workflow di Deep Learning nei settori del Machine Learning informato dalla fisica (PIML) e delle reti neurali informate dalla fisica (PINN)

Utilizzare Deep Learning Toolbox™ per il Machine Learning informato dalla fisica (PIML) e le reti neurali informate dalla fisica (PINN).

Il Machine Learning informato dalla fisica (PIML) e le reti neurali informate dalla fisica sono concetti di Machine Learning e Deep Learning che consentono di integrare leggi e principi dei sistemi fisici nei modelli di Machine Learning. L'integrazione di questi concetti può migliorare la precisione e la robustezza di tali modelli e contribuire a garantire che anche le previsioni dei modelli rispettino tali leggi e principi. Ad esempio, è possibile addestrare una rete neurale che modella il trasferimento di calore utilizzando una funzione di perdita che incorpora le leggi della termodinamica.

Funzioni

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Livelli della rete neurale

`neuralODELayer`	Neural ODE layer (Da R2023b)
`spectralConvolution1dLayer`	1-D spectral convolutional layer (Da R2026a)
`spectralConvolution2dLayer`	2-D spectral convolutional layer (Da R2026a)
`spectralConvolution3dLayer`	3-D spectral convolutional layer (Da R2026a)
`complexToRealLayer`	Complex-to-real layer (Da R2024b)
`realToComplexLayer`	Real-to-complex layer (Da R2024b)
`complexFullyConnectedLayer`	Complex fully connected layer (Da R2026a)
`complexReluLayer`	Complex rectified linear unit (ReLU) layer (Da R2025a)

Differenziazione automatica

`dlarray`	Deep learning array for customization
`dlgradient`	Compute gradients for custom training loops using automatic differentiation
`dljacobian`	Jacobian matrix deep learning operation (Da R2024b)
`dldivergence`	Divergence of deep learning data (Da R2024b)
`dllaplacian`	Laplacian of deep learning data (Da R2024b)
`dlfeval`	Evaluate deep learning model for custom training loops
`dlode45`	Deep learning solution of nonstiff ordinary differential equation (ODE) (Da R2021b)

Argomenti

Solve PDE Using Fourier Neural Operator
This example shows how to train a Fourier neural operator (FNO) neural network that outputs the solution of a partial differential equation (PDE).
Solve PDE Using Physics-Informed Neural Network
This example shows how to train a physics-informed neural network (PINN) to predict the solutions of a partial differential equation (PDE).
Solve ODE Using Physics-Informed Neural Network
This example shows how to train a physics-informed neural network (PINN) to predict the solutions of an ordinary differential equation (ODE).
Train Latent ODE Network with Irregularly Sampled Time-Series Data
This example shows how to train a latent ordinary differential equation (ODE) autoencoder with time-series data that is sampled at irregular time intervals.
Dynamical System Modeling Using Neural ODE
This example shows how to train a neural network with neural ordinary differential equations (ODEs) to learn the dynamics of a physical system.
Train Neural ODE Network with Control Input
This example shows how to train a neural ODE that models a swinging pendulum with torque input. (Da R2026a)
Solve Inverse Problem for PDE Using Physics-Informed Neural Network
This example shows how to solve an inverse problem using a physics-informed neural network (PINN). (Da R2025a)
Solve Poisson Equation on Unit Disk Using Physics-Informed Neural Networks (Partial Differential Equation Toolbox)
Solve a Poisson's equation with Dirichlet boundary conditions using a physics-informed neural network (PINN).

Informazioni complementari

Machine Learning scientifico e informato dalla fisica in MATLAB (GitHub)

Esempi in primo piano

Solve Heat Equation Using Graph Neural Network

Solve a heat equation with using a graph neural network (GNN).

(Partial Differential Equation Toolbox)

Da R2025a

Nuova

3-D Battery Module Cooling Analysis Using Fourier Neural Operator

Model three-dimensional heat diffusion in a battery module using a Fourier neural operator (FNO) neural network.

(Partial Differential Equation Toolbox)

Da R2026a