Publication

A framework to solve inverse problems for parametric PDEs using adaptive finite elements and neural networks

Marco Picasso
2025

Abstract

Parameter identification is important in many engineering processes, and benefits from quick evaluations with reduced models. We present here a framework to solve inverse problems for parametric partial differential equations. The reduced model is built on a neural network method for the numerical approximation of a given parametric partial differential equation. Training data are generated thanks to adaptive finite element simulations. A supervised feedforward neural network is then used for the online approximation of the solution. The inverse problem aims at identifying parameters using available measurement data. The corresponding optimization problem is solved with a particle swarm optimization method. Numerical results are presented for the parameter identification of several elliptic and hyperbolic model problems.

Official source

https://infoscience.epfl.ch/entities/publication/6cec34b6-1d94-4168-a5df-3b047d59f1fb

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Marco Picasso
2025

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/6cec34b6-1d94-4168-a5df-3b047d59f1fb

About this result

Related concepts (32)

Artificial neural network

Artificial neural networks (ANNs, also shortened to neural networks (NNs) or neural nets) are a branch of machine learning models that are built using principles of neuronal organization discovered by connectionism in the biological neural networks constituting animal brains. An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons.

Types of artificial neural networks

There are many types of artificial neural networks (ANN). Artificial neural networks are computational models inspired by biological neural networks, and are used to approximate functions that are generally unknown. Particularly, they are inspired by the behaviour of neurons and the electrical signals they convey between input (such as from the eyes or nerve endings in the hand), processing, and output from the brain (such as reacting to light, touch, or heat). The way neurons semantically communicate is an area of ongoing research.

Recurrent neural network

A recurrent neural network (RNN) is one of the two broad types of artificial neural network, characterized by direction of the flow of information between its layers. In contrast to uni-directional feedforward neural network, it is a bi-directional artificial neural network, meaning that it allows the output from some nodes to affect subsequent input to the same nodes. Their ability to use internal state (memory) to process arbitrary sequences of inputs makes them applicable to tasks such as unsegmented, connected handwriting recognition or speech recognition.

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A framework to solve inverse problems for parametric PDEs using adaptive finite elements and neural networks

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