Related papers: GPLaSDI: Gaussian Process-based Interpretable Late…

We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…

We present a quadrotor dynamics Gaussian Process (GP) with gradient information that achieves real-time inference via state-space partitioning and approximation, and that includes aerodynamic effects using data from mid-fidelity potential…

Adaptive learning is necessary for non-stationary environments where the learning machine needs to forget past data distribution. Efficient algorithms require a compact model update to not grow in computational burden with the incoming data…

Partial differential equations (PDEs) have become an essential tool for modeling complex physical systems. Such equations are typically solved numerically via mesh-based methods, such as finite element methods, with solutions over the…

We put forward a new Bayesian modeling strategy for spatiotemporal count data that enables efficient posterior sampling. Most previous models for such data decompose logarithms of the response Poisson rates into fixed effects and spatial…

Accurate human motion prediction with well-calibrated uncertainty is critical for safe human-robot collaboration (HRC), where robots must anticipate and react to human movements in real time. We propose a structured multitask variational…

Gaussian Process (GP) regressions have proven to be a valuable tool to predict disturbances and model mismatches and incorporate this information into a Model Predictive Control (MPC) prediction. Unfortunately, the computational complexity…

The Gaussian Process Latent Variable Model (GP-LVM) is a non-linear probabilistic method of embedding a high dimensional dataset in terms low dimensional `latent' variables. In this paper we illustrate that maximum a posteriori (MAP)…

Identification of parameters in ordinary differential equations (ODEs) is an important and challenging task when modeling dynamic systems in biomedical research and other scientific areas, especially with the presence of time-varying…

High-dimensional optimization is a critical challenge for operating large-scale scientific facilities. We apply a physics-informed Gaussian process (GP) optimizer to tune a complex system by conducting efficient global search. Typical GP…

Solving partial differential equations (PDEs) serves as a cornerstone for modeling complex dynamical systems. Recent progresses have demonstrated grand benefits of data-driven neural-based models for predicting spatiotemporal dynamics…

I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…

The goal of system identification is to learn about underlying physics dynamics behind the time-series data. To model the probabilistic and nonparametric dynamics model, Gaussian process (GP) have been widely used; GP can estimate the…

Gaussian processes (GPs) are non-parametric probabilistic regression models that are popular due to their flexibility, data efficiency, and well-calibrated uncertainty estimates. However, standard GP models assume homoskedastic Gaussian…

Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…

Physical systems can often be described via a continuous-time dynamical system. In practice, the true system is often unknown and has to be learned from measurement data. Since data is typically collected in discrete time, e.g. by sensors,…

This paper presents a probabilistic framework to obtain both reliable and fast uncertainty estimates for predictions with Deep Neural Networks (DNNs). Our main contribution is a practical and principled combination of DNNs with sparse…

We propose a novel Stochastic Differential Equation (SDE) framework to address the problem of learning uncertainty-aware representations for graph-structured data. While Graph Neural Ordinary Differential Equations (GNODEs) have shown…

A key challenge with controlling complex dynamical systems is to accurately model them. However, this requirement is very hard to satisfy in practice. Data-driven approaches such as Gaussian processes (GPs) have proved quite effective by…

Multi-fidelity modeling and calibration are data fusion tasks that ubiquitously arise in engineering design. In this paper, we introduce a novel approach based on latent-map Gaussian processes (LMGPs) that enables efficient and accurate…