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We introduce an ordinary differential equation (ODE) based deep generative method for learning conditional distributions, named Conditional F\"ollmer Flow. Starting from a standard Gaussian distribution, the proposed flow could approximate…
The core objective of machine-assisted scientific discovery is to learn physical laws from experimental data without prior knowledge of the systems in question. In the area of quantum physics, making progress towards these goals is…
High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphics (motion capture data). Practical nonlinear…
What do data tell us about physics-and what don't they tell us? There has been a surge of interest in using machine learning models to discover governing physical laws such as differential equations from data, but current methods lack…
Leveraging autonomous systems in safety-critical scenarios requires verifying their behaviors in the presence of uncertainties and black-box components that influence the system dynamics. In this work, we develop a framework for verifying…
Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…
This article is concerned with learning and stochastic control in physical systems which contain unknown input signals. These unknown signals are modeled as Gaussian processes (GP) with certain parametrized covariance structures. The…
System inference for nonlinear dynamic models, represented by ordinary differential equations (ODEs), remains a significant challenge in many fields, particularly when the data are noisy, sparse, or partially observable. In this paper, we…
We introduce a Gaussian process-based model for handling of non-stationarity. The warping is achieved non-parametrically, through imposing a prior on the relative change of distance between subsequent observation inputs. The model allows…
This work aims to improve generalization and interpretability of dynamical systems by recovering the underlying lower-dimensional latent states and their time evolutions. Previous work on disentangled representation learning within the…
Modeling the evolution of system with time-series data is a challenging and critical task in a wide range of fields, especially when the time-series data is regularly sampled and partially observable. Some methods have been proposed to…
Gaussian processes provide a compact representation for modeling and estimating an unknown function, that can be updated as new measurements of the function are obtained. This paper extends this powerful framework to the case where the…
This paper presents a data-driven algorithm for simultaneous system identification and parameter estimation in control-affine nonlinear systems. Parameter estimation is achieved by training a data-driven predictive model using state-action…
A long-standing problem at the interface of artificial intelligence and applied mathematics is to devise an algorithm capable of achieving human level or even superhuman proficiency in transforming observed data into predictive mathematical…
Analysis of heterogeneous patterns in complex spatio-temporal data finds usage across various domains in applied science and engineering, including training autonomous vehicles to navigate in complex traffic scenarios. Motivated by…
The application of Stochastic Differential Equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we…
We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unknown, bursts of observation data of the slow variables are…
Discovering governing equations from data is crucial for understanding complex systems in many diverse fields from science to engineering. Yet, there still is a lack of versatile computational toolbox to deal with this long standing…
Recently, Neural Ordinary Differential Equations has emerged as a powerful framework for modeling physical simulations without explicitly defining the ODEs governing the system, but instead learning them via machine learning. However, the…
Machine-learning driven models have proven to be powerful tools for the identification of phases of matter. In particular, unsupervised methods hold the promise to help discover new phases of matter without the need for any prior…