Related papers: Learning to simulate partially known spatio-tempor…

We introduce Neural Dynamical Systems (NDS), a method of learning dynamical models in various gray-box settings which incorporates prior knowledge in the form of systems of ordinary differential equations. NDS uses neural networks to…

Despite the growing prevalence of black-box pre-trained models (PTMs) such as prediction API services, there remains a significant challenge in directly applying general models to real-world scenarios due to the data distribution gap.…

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…

Recent advancements in operator-type neural networks have shown promising results in approximating the solutions of spatiotemporal Partial Differential Equations (PDEs). However, these neural networks often entail considerable training…

The ubiquity of neural networks (NNs) in real-world applications, from healthcare to natural language processing, underscores their immense utility in capturing complex relationships within high-dimensional data. However, NNs come with…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

We present an integrated Task-Motion Planning framework for robot navigation in belief space. Autonomous robots operating in real world complex scenarios require planning in the discrete (task) space and the continuous (motion) space. To…

This paper proposes a distributed data-driven framework for dynamics learning, termed distributed deep Koopman learning using partial trajectories (DDKL-PT). In this framework, each agent in a multi-agent system is assigned a partial…

Several low-bandwidth distributable black-box optimization algorithms in the family of finite differences such as Evolution Strategies have recently been shown to perform nearly as well as tailored Reinforcement Learning methods in some…

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…

Model-based reinforcement learning (MBRL) algorithms can attain significant sample efficiency but require an appropriate network structure to represent system dynamics. Current approaches include white-box modeling using analytic…

Ocean current, fluid mechanics, and many other spatio-temporal physical dynamical systems are essential components of the universe. One key characteristic of such systems is that certain physics laws -- represented as ordinary/partial…

The paper proposes the ScatterNet Hybrid Deep Learning (SHDL) network that extracts invariant and discriminative image representations for object recognition. SHDL framework is constructed with a multi-layer ScatterNet front-end, an…

Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…

Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high…

Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

There is a rising interest in Spatio-temporal systems described by Partial Differential Equations (PDEs) among the control community. Not only are these systems challenging to control, but the sizing and placement of their actuation is an…

While recurrent neural networks (RNNs) demonstrate outstanding capabilities for future video frame prediction, they model dynamics in a discrete time space, i.e., they predict the frames sequentially with a fixed temporal step. RNNs are…

We present that, instead of establishing the equations of motion, one can model-freely reveal the dynamical properties of a black-box system using a learning machine. Trained only by a segment of time series of a state variable recorded at…