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Machine learning algorithms designed to learn dynamical systems from data can be used to forecast, control and interpret the observed dynamics. In this work we exemplify the use of one of such algorithms, namely Koopman operator learning,…
Accurately modeling robot dynamics is crucial to safe and efficient motion control. In this paper, we develop and apply an iterative learning semi-parametric model, with a neural network, to the task of autonomous racing with a Model…
In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and…
Conditional diffusion models provide a natural framework for probabilistic prediction of dynamical systems and have been successfully applied to fluid dynamics and weather prediction. However, in many settings, the available information at…
The estimation of static parameters in dynamical systems and control theory has been extensively studied, with significant progress made in estimating varying parameters in specific system types. Suppose, in the general case, we have data…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
In many complex molecular systems, the macroscopic ensemble's properties are controlled by microscopic dynamic events (or fluctuations) that are often difficult to detect via pattern-recognition approaches. Discovering the relationships…
Multivariate functional data from a complex system are naturally high-dimensional and have complex cross-correlation structure. The complexity of data structure can be observed as that (1) some functions are strongly correlated with similar…
Investigating the dynamics of learning in machine learning algorithms is of paramount importance for understanding how and why an approach may be successful. The tools of physics and statistics provide a robust setting for such…
Automated model selection is an important application in science and engineering. In this work, we develop a learning approach for identifying structured dynamical systems from undersampled and noisy spatiotemporal data. The learning is…
We describe a stochastic, dynamical system capable of inference and learning in a probabilistic latent variable model. The most challenging problem in such models - sampling the posterior distribution over latent variables - is proposed to…
This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques. The proposed framework reformulates the prediction problem as a supervised learning problem to…
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…
Recently there has been substantial interest in spectral methods for learning dynamical systems. These methods are popular since they often offer a good tradeoff between computational and statistical efficiency. Unfortunately, they can be…
Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has become increasingly popular for simulating posterior samples in large-scale Bayesian modeling. However, existing SG-MCMC schemes are not tailored to any specific probabilistic…
There are two major challenges for scaling up robot navigation around dynamic obstacles: the complex interaction dynamics of the obstacles can be hard to model analytically, and the complexity of planning and control grows exponentially in…
Molecular Dynamics (MD) simulations are fundamental computational tools for the study of proteins and their free energy landscapes. However, sampling protein conformational changes through MD simulations is challenging due to the relatively…
Data assimilation algorithms estimate the state of a dynamical system from partial observations, where the successful performance of these algorithms hinges on costly parameter tuning and on employing an accurate model for the dynamics.…
A driving algorithm that aligns with good human driving practices, or at the very least collaborates effectively with human drivers, is crucial for developing safe and efficient autonomous vehicles. In practice, two main approaches are…
A fundamental challenge in developing data-driven approaches to ecological systems for tasks such as state estimation and prediction is the paucity of the observational or measurement data. For example, modern machine-learning techniques…