Related papers: PDE Control Gym: A Benchmark for Data-Driven Bound…

Model-free algorithms are brought into the control system's research with the emergence of reinforcement learning algorithms. However, there are two practical challenges of reinforcement learning-based methods. First, learning by…

Deep Reinforcement Learning has enabled the control of increasingly complex and high-dimensional problems. However, the need of vast amounts of data before reasonable performance is attained prevents its widespread application. We employ…

Reinforcement learning has emerged as a promising methodology for training robot controllers. However, most results have been limited to simulation due to the need for a large number of samples and the lack of automated-yet-safe data…

The approximation of solutions of partial differential equations (PDEs) with numerical algorithms is a central topic in applied mathematics. For many decades, various types of methods for this purpose have been developed and extensively…

We develop a control algorithm that ensures the safety, in terms of confinement in a set, of a system with unknown, 2nd-order nonlinear dynamics. The algorithm establishes novel connections between data-driven and robust, nonlinear control.…

Partial Differential Equations (PDEs) describe phenomena ranging from turbulence and epidemics to quantum mechanics and financial markets. Despite recent advances in computational science, solving such PDEs for real-world applications…

Modeling complex spatiotemporal dynamical systems, such as the reaction-diffusion processes, have largely relied on partial differential equations (PDEs). However, due to insufficient prior knowledge on some under-explored dynamical…

We present a framework and algorithms to learn controlled dynamics models using neural stochastic differential equations (SDEs) -- SDEs whose drift and diffusion terms are both parametrized by neural networks. We construct the drift term to…

Unveiling the underlying governing equations of nonlinear dynamic systems remains a significant challenge. Insufficient prior knowledge hinders the determination of an accurate candidate library, while noisy observations lead to imprecise…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding physical laws into neural network training. However, traditional PINN models are typically designed…

The recently introduced DeepONet operator-learning framework for PDE control is extended from the results for basic hyperbolic and parabolic PDEs to an advanced hyperbolic class that involves delays on both the state and the system output…

We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…

In recent years several learning approaches to point goal navigation in previously unseen environments have been proposed. They vary in the representations of the environments, problem decomposition, and experimental evaluation. In this…

We develop a delay-adaptive controller for a class of first-order hyperbolic partial integro-differential equations (PIDEs) with an unknown input delay. By employing a transport PDE to represent delayed actuator states, the system is…

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…

The measured spatiotemporal response of various physical processes is utilized to infer the governing partial differential equations (PDEs). We propose SimultaNeous Basis Function Approximation and Parameter Estimation (SNAPE), a technique…

This paper presents a novel neural operator learning framework for designing boundary control to mitigate stop-and-go congestion on freeways. The freeway traffic dynamics are described by second-order coupled hyperbolic partial differential…

Physics-informed deep learning often faces optimization challenges due to the complexity of solving partial differential equations (PDEs), which involve exploring large solution spaces, require numerous iterations, and can lead to unstable…

Several recent works in scientific machine learning have revived interest in the application of neural networks to partial differential equations (PDEs). A popular approach is to aggregate the residual form of the governing PDE and its…

Partial differential equations (PDEs) govern physical phenomena across the full range of scientific scales, yet their computational solution remains one of the defining challenges of modern science. This critical review examines two mature…