Related papers: Operator learning for prescribed-time stabilizatio…
This paper introduces a fast and numerically stable algorithm for the solution of fourth-order linear boundary value problems on an interval. This type of equation arises in a variety of settings in physics and signal processing. Our method…
Diffusion models have recently emerged as powerful stochastic frameworks for high-dimensional inference and generation. However, existing applications to partial differential equations (PDEs) predominantly rely on physics-informed training…
Systems modeled by partial differential equations (PDEs) are at least as ubiquitous as systems that are by nature finite-dimensional and modeled by ordinary differential equations (ODEs). And yet, systematic and readily usable…
We develop a novel multi-layer predictor-feedback to achieve exact compensation of state-dependent input delay of general nonlinear integro-differential equations. The system of interest is an unconventional mixed Partial Differential…
In this paper, we present a rapid boundary stabilization of a Timoshenko beam with anti-damping and anti-stiffness at the uncontrolled boundary, by using PDE backstepping. We introduce a transformation to map the Timoshenko beam states into…
In this paper, we consider the boundary stabilization and observation of the multidimensional unstable heat equation. Since we consider the heat equation in a general domain, the usual partial differential equation back-stepping method is…
Operator learning has emerged as a powerful tool in scientific computing for approximating mappings between infinite-dimensional function spaces. A primary application of operator learning is the development of surrogate models for the…
This work introduces and rigorously analyzes a novel operator-splitting finite element scheme for approximating viscosity solutions of a broad class of constrained second-order partial differential equations. By decoupling the primary PDE…
Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…
Training Neural Ordinary Differential Equations (ODEs) is often computationally expensive. Indeed, computing the forward pass of such models involves solving an ODE which can become arbitrarily complex during training. Recent works have…
This article provides a rigorous analysis of convergence and stability of Episodic Upside-Down Reinforcement Learning, Goal-Conditioned Supervised Learning and Online Decision Transformers. These algorithms performed competitively across…
This paper studies the problem of designing sampled-data observers and observer-based, sampled-data, output feedback stabilizers for systems with both discrete and distributed, state and output time-delays. The obtained results can be…
We consider nonlinear inverse problems arising in the context of parameter identification for parabolic partial differential equations (PDEs). For stable reconstructions, regularization methods such as the iteratively regularized…
This letter presents a unified framework for the design of prescribed-time controllers under time-varying input and state constraints for normal-form unknown nonlinear systems with uncertain input gain. The proposed approach is based on a…
This study investigates a strongly-coupled system of partial differential equations (PDE) governing heat transfer in a copper rod, longitudinal vibrations, and total charge accumulation at electrodes within a magnetizable piezoelectric…
The modeling and control of single-phase flow systems governed by Partial Differential Equations (PDEs) present challenges, especially under transient conditions. In this work, we extend the Physics-Informed Neural Nets for Control (PINC)…
Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based…
We present PDE-FM, a modular foundation model for physics-informed machine learning that unifies spatial, spectral, and temporal reasoning across heterogeneous partial differential equation (PDE) systems. PDE-FM combines spatial-spectral…
Recently, the use of neural networks to accelerate the solving of partial differential equations (PDEs) has gained significant traction in both academia and industry. However, employing neural networks as standalone surrogate models raises…
Stabilization of a coupled system consisting of a parabolic partial differential equation and an elliptic partial differential equation is considered. Even in the situation when the parabolic equation is exponentially stable on its own, the…