Related papers: On Learning the Dynamical Response of Nonlinear Co…

Discovering the underlying behavior of complex systems is an important topic in many science and engineering disciplines. In this paper, we propose a novel neural network framework, finite difference neural networks (FDNet), to learn…

We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…

Planning has been very successful for control tasks with known environment dynamics. To leverage planning in unknown environments, the agent needs to learn the dynamics from interactions with the world. However, learning dynamics models…

In numerous contexts, high-resolution solutions to partial differential equations are required to capture faithfully essential dynamics which occur at small spatiotemporal scales, but these solutions can be very difficult and slow to obtain…

Applying Deep Learning to control has a lot of potential for enabling the intelligent design of robot control laws. Unfortunately common deep learning approaches to control, such as deep reinforcement learning, require an unrealistic amount…

A properly designed controller can help improve the quality of experimental measurements or force a dynamical system to follow a completely new time-evolution path. Recent developments in deep reinforcement learning have made steep advances…

The Physics-Constrained DeepONet (PC-DeepONet), an architecture that incorporates fundamental physics knowledge into the data-driven DeepONet model, is presented in this study. This methodology is exemplified through surrogate modeling of…

Existing motion planning methods often struggle with rapid-motion obstacles due to an insufficient understanding of environmental changes. To address this, we propose integrating motion planners with Doppler LiDARs, which provide not only…

Deep operator networks (DeepONets) are receiving increased attention thanks to their demonstrated capability to approximate nonlinear operators between infinite-dimensional Banach spaces. However, despite their remarkable early promise,…

To speed-up the solution to parametrized differential problems, reduced order models (ROMs) have been developed over the years, including projection-based ROMs such as the reduced-basis (RB) method, deep learning-based ROMs, as well as…

The fundamental lemma from behavioral systems theory yields a data-driven non-parametric system representation that has shown great potential for the data-efficient control of unknown linear and weakly nonlinear systems, even in the…

Recent work has attempted to interpret residual networks (ResNets) as one step of a forward Euler discretization of an ordinary differential equation, focusing mainly on syntactic algebraic similarities between the two systems. Discrete…

In this work, we propose an effective scheme (called DP-Net) for compressing the deep neural networks (DNNs). It includes a novel dynamic programming (DP) based algorithm to obtain the optimal solution of weight quantization and an…

Currently decision making is one of the biggest challenges in autonomous driving. This paper introduces a method for safely navigating an autonomous vehicle in highway scenarios by combining deep Q-Networks and insight from control theory.…

Learning time-dependent partial differential equations (PDEs) that govern evolutionary observations is one of the core challenges for data-driven inference in many fields. In this work, we propose to capture the essential dynamics of…

Operator learning has the potential to strongly impact scientific computing by learning solution operators for differential equations, potentially accelerating multi-query tasks such as design optimization and uncertainty quantification by…

Deep residual networks (ResNets) and their variants are widely used in many computer vision applications and natural language processing tasks. However, the theoretical principles for designing and training ResNets are still not fully…

Deep learning techniques have shown promise in many domain applications. This paper proposes a novel deep reservoir computing framework, termed deep recurrent stochastic configuration network (DeepRSCN) for modelling nonlinear dynamic…

Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…

This paper addresses reinforcement learning based, direct signal tracking control with an objective of developing mathematically suitable and practically useful design approaches. Specifically, we aim to provide reliable and easy to…