5 papers
Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems
Zhen Zhang, Alessandro Alla, George Em Karniadakis
Inverse problems governed by partial differential equations (PDEs) are central to computational mechanics and are commonly solved by adjoint-based optimization, while physics-infor…
PINNs in PDE Constrained Optimal Control Problems: Direct vs Indirect Methods
Zhen Zhang, Shanqing Liu, Alessandro Alla +2
We study physics-informed neural networks (PINNs) as numerical tools for the optimal control of semilinear partial differential equations. We first recall the classical direct and…
Discovery of interaction and diffusion kernels in particle-to-mean-field multi-agent systems
Giacomo Albi, Alessandro Alla, Elisa Calzola
We propose a data-driven framework to learn interaction kernels in stochastic multi-agent systems. Our approach aims at identifying the functional form of nonlocal interaction and…
A PINN approach for the online identification and control of unknown PDEs
Alessandro Alla, Giulia Bertaglia, Elisa Calzola
Physics-Informed Neural Networks (PINNs) have revolutionized solving differential equations by integrating physical laws into neural networks training. This paper explores PINNs fo…
A POD approach to identify and control PDEs online through State Dependent Riccati equations
Alessandro Alla, Agnese Pacifico
We address the control of Partial Differential equations (PDEs) with unknown parameters. Our objective is to devise an efficient algorithm capable of both identifying and controlli…