相关论文: Deep Latent Force Models: ODE-based Process Convol…

In recent years, deep learning has proven to be a viable methodology for surrogate modeling and uncertainty quantification for a vast number of physical systems. However, in their traditional form, such models can require a large amount of…

Datasets that exhibit non-Gaussian characteristics are common in many fields, while the current modeling framework and available software for non-Gaussian models is limited. We introduce Linear Latent Non-Gaussian Models (LLnGMs), a unified…

Neural Linear Models (NLM) are deep Bayesian models that produce predictive uncertainties by learning features from the data and then performing Bayesian linear regression over these features. Despite their popularity, few works have…

Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with…

Recently, a novel linear model predictive control algorithm based on a physics-informed Gaussian Process has been introduced, whose realizations strictly follow a system of underlying linear ordinary differential equations with constant…

Latent force models are systems whereby there is a mechanistic model describing the dynamics of the system state, with some unknown forcing term that is approximated with a Gaussian process. If such dynamics are non-linear, it can be…

We propose a novel probabilistic framework, termed LVM-GP, for uncertainty quantification in solving forward and inverse partial differential equations (PDEs) with noisy data. The core idea is to construct a stochastic mapping from the…

We revisit the Bayesian online inference problems for the linear dynamic systems (LDS) under non- Gaussian environment. The noises can naturally be non-Gaussian (skewed and/or heavy tailed) or to accommodate spurious observations, noises…

Dynamic systems described by differential equations often involve feedback among system components. When there are time delays for components to sense and respond to feedback, delay differential equation (DDE) models are commonly used. This…

We present DeepFDM, a differentiable finite-difference framework for learning spatially varying coefficients in time-dependent partial differential equations (PDEs). By embedding a classical forward-Euler discretization into a convolutional…

Regression models are used for inference and prediction in a wide range of applications providing a powerful scientific tool for researchers and analysts from different fields. In many research fields the amount of available data as well as…

Accuracy and generalization capabilities are key objectives when learning dynamical system models. To obtain such models from limited data, current works exploit prior knowledge and assumptions about the system. However, the fusion of…

High-fidelity modeling of turbulent flows is one of the major challenges in computational physics, with diverse applications in engineering, earth sciences and astrophysics, among many others. The rising popularity of high-fidelity…

We present a non-parametric Bayesian latent variable model capable of learning dependency structures across dimensions in a multivariate setting. Our approach is based on flexible Gaussian process priors for the generative mappings and…

The identification of Linear Time-Varying (LTV) systems from input-output data is a fundamental yet challenging ill-posed inverse problem. This work introduces a unified Bayesian framework that models the system's impulse response, $h(t,…

Nonlinear dynamical systems with input delays pose significant challenges for prediction, estimation, and control due to their inherent complexity and the impact of delays on system behavior. Traditional linear control techniques often fail…

Physical systems whose dynamics are governed by partial differential equations (PDEs) find applications in numerous fields, from engineering design to weather forecasting. The process of obtaining the solution from such PDEs may be…

Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to…

Discrete latent factor models (DLFMs) are widely used in various domains such as machine learning, economics, neuroscience, psychology, etc. Currently, fitting a DLFM to some dataset relies on a customized solver for individual models,…

Planning is a powerful approach to control problems with known environment dynamics. In unknown environments the agent needs to learn a model of the system dynamics to make planning applicable. This is particularly challenging when the…