Related papers: Solving PDE-constrained Control Problems Using Ope…

Optimal control provides a principled framework for transforming dynamical system models into intelligent decision-making, yet classical computational approaches are often too expensive for real-time deployment in dynamic or uncertain…

This paper explores continuous-time and state-space optimal stopping problems from a reinforcement learning perspective. We begin by formulating the stopping problem using randomized stopping times, where the decision maker's control is…

Although there is a substantial body of literature on control and optimization problems for parabolic and hyperbolic systems, the specific problem of controlling and optimizing the coefficients of the associated operators within such…

We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…

Learning solution operators for differential equations with neural networks has shown great potential in scientific computing, but ensuring their stability under input perturbations remains a critical challenge. This paper presents a robust…

A kernel-based approach for the learning of the solution operator of general nonhomogeneous partial differential equations (PDEs) is proposed. The method incorporates physical priors, typically encoded through the PDE operator, into a…

PDE-Constrained Optimization (PDECO) problems can be accelerated significantly by employing gradient-based methods with surrogate models like neural operators compared to traditional numerical solvers. However, this approach faces two key…

Predicting outcomes and planning interactions with the physical world are long-standing goals for machine learning. A variety of such tasks involves continuous physical systems, which can be described by partial differential equations…

We consider numerical approaches for deterministic, finite-dimensional optimal control problems whose dynamics depend on unknown or uncertain parameters. We seek to amortize the solution over a set of relevant parameters in an offline stage…

Deep Operator Networks are emerging as fundamental tools among various neural network types to learn mappings between function spaces, and have recently gained attention due to their ability to approximate nonlinear operators. In…

In this work, we consider an optimal control problem subject to a nonlinear PDE constraint and apply it to the regularized $p$-Laplace equation. To this end, a reduced unconstrained optimization problem in terms of the control variable is…

We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…

We investigate an optimization problem governed by an elliptic partial differential equation with uncertain parameters. We introduce a robust optimization framework that accounts for uncertain model parameters. The resulting non-linear…

We consider a general class of nonsmooth optimal control problems with partial differential equation (PDE) constraints, which are very challenging due to its nonsmooth objective functionals and the resulting high-dimensional and…

Embedding physical knowledge into neural network (NN) training has been a hot topic. However, when facing the complex real-world, most of the existing methods still strongly rely on the quantity and quality of observation data. Furthermore,…

A fundamental problem in science and engineering is designing optimal control policies that steer a given system towards a desired outcome. This work proposes Control Physics-Informed Neural Networks (Control PINNs) that simultaneously…

We propose a partial differential-integral equation (PDE) framework for deep neural networks (DNNs) and their associated learning problem by taking the continuum limits of both network width and depth. The proposed model captures the…

Optimal actuator and control design is studied as a multi-level optimisation problem, where the actuator design is evaluated based on the performance of the associated optimal closed loop. The evaluation of the optimal closed loop for a…

Many real-world systems are modelled using complex ordinary differential equations (ODEs). However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like Proper Orthogonal…

This paper presents a novel methodology to tackle feedback optimal control problems in scenarios where the exact state of the controlled process is unknown. It integrates data assimilation techniques and optimal control solvers to manage…