Related papers: Neural ODE and SDE Models for Adaptation and Plann…

Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…

Owing to the remarkable development of deep learning technology, there have been a series of efforts to build deep learning-based climate models. Whereas most of them utilize recurrent neural networks and/or graph neural networks, we design…

Latent ODE models provide flexible descriptions of dynamic systems, but they can struggle with extrapolation and predicting complicated non-linear dynamics. The latent ODE approach implicitly relies on encoders to identify unknown system…

Learning network dynamics from the empirical structure and spatio-temporal observation data is crucial to revealing the interaction mechanisms of complex networks in a wide range of domains. However, most existing methods only aim at…

A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…

The choice of how to retain information about past gradients dramatically affects the convergence properties of state-of-the-art stochastic optimization methods, such as Heavy-ball, Nesterov's momentum, RMSprop and Adam. Building on this…

Route planning is essential to mobile robot navigation problems. In recent years, deep reinforcement learning (DRL) has been applied to learning optimal planning policies in stochastic environments without prior knowledge. However, existing…

The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin.…

A computed approximation of the solution operator to a system of partial differential equations (PDEs) is needed in various areas of science and engineering. Neural operators have been shown to be quite effective at predicting these…

We investigate the task of learning to follow natural language instructions by jointly reasoning with visual observations and language inputs. In contrast to existing methods which start with learning from demonstrations (LfD) and then use…

We present an algorithm for model-based reinforcement learning that combines Bayesian neural networks (BNNs) with random roll-outs and stochastic optimization for policy learning. The BNNs are trained by minimizing $\alpha$-divergences,…

We propose the *State Space Neural Operator* (SS-NO), a compact architecture for learning solution operators of time-dependent partial differential equations (PDEs). Our formulation extends structured state space models (SSMs) to joint…

Stemming from the stochastic Lotka-Volterra or predator-prey equations, this work aims to model the spatial inhomogeneity by using stochastic partial differential equations (SPDEs). Compared to the classical models, the SPDE model is more…

This paper presents the Standalone Neural ODE (sNODE), a continuous-depth neural ODE model capable of describing a full deep neural network. This uses a novel nonlinear conjugate gradient (NCG) descent optimization scheme for training,…

We present a falsification framework that integrates learned surrogate dynamics with optimal control to efficiently generate counterexamples for cyber-physical systems specified in signal temporal logic (STL). The unknown system dynamics…

Modeling the traffic dynamics is essential for understanding and predicting the traffic spatiotemporal evolution. However, deriving the partial differential equation (PDE) models that capture these dynamics is challenging due to their…

In this paper we establish a connection between non-convex optimization methods for training deep neural networks and nonlinear partial differential equations (PDEs). Relaxation techniques arising in statistical physics which have already…

We propose a method to reproduce dynamic appearance textures with space-stationary but time-varying visual statistics. While most previous work decomposes dynamic textures into static appearance and motion, we focus on dynamic appearance…

Training dynamic models, such as neural ODEs, on long trajectories is a hard problem that requires using various tricks, such as trajectory splitting, to make model training work in practice. These methods are often heuristics with poor…

We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…