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

An approach for the identification of discontinuous and nonsmooth nonlinear forces, as those generated by frictional contacts, in mechanical systems that can be approximated by a single-degree-of-freedom model is presented. To handle the…

Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic…

The modelling of Earth observation data is a challenging problem, typically approached by either purely mechanistic or purely data-driven methods. Mechanistic models encode the domain knowledge and physical rules governing the system. Such…

Physically-inspired latent force models offer an interpretable alternative to purely data driven tools for inference in dynamical systems. They carry the structure of differential equations and the flexibility of Gaussian processes,…

In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality…

Latent force models (LFM) are principled approaches to incorporating solutions to differential equations within non-parametric inference methods. Unfortunately, the development and application of LFMs can be inhibited by their computational…

Purely data driven approaches for machine learning present difficulties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to…

The problem of combined state and input estimation of linear structural systems based on measured responses and a priori knowledge of structural model is considered. A novel methodology using Gaussian process latent force models is proposed…

Learning mappings between functional spaces, also known as function-on-function regression, is a fundamental problem in functional data analysis with broad applications, including spatiotemporal forecasting, curve prediction, and climate…

Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…

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

We introduce a physics-driven deep latent variable model (PDDLVM) to learn simultaneously parameter-to-solution (forward) and solution-to-parameter (inverse) maps of parametric partial differential equations (PDEs). Our formulation…

A latent force model is a Gaussian process with a covariance function inspired by a differential operator. Such covariance function is obtained by performing convolution integrals between Green's functions associated to the differential…

In this paper, we propose a domain-decomposition-based deep learning (DL) framework, named transient-CoMLSim, for accurately modeling unsteady and nonlinear partial differential equations (PDEs). The framework consists of two key…

A novel deep neural network framework -- that we refer to as Deep Dynamic Factor Model (D$^2$FM) --, is able to encode the information available, from hundreds of macroeconomic and financial time-series into a handful of unobserved latent…

We propose a new approach to inverse reinforcement learning (IRL) based on the deep Gaussian process (deep GP) model, which is capable of learning complicated reward structures with few demonstrations. Our model stacks multiple latent GP…

The development of robust generative models for highly varied non-stationary time series data is a complex yet important problem. Traditional models for time series data prediction, such as Long Short-Term Memory (LSTM), are inefficient and…

In nonlinear latent variable models or dynamic models, if we consider the latent variables as confounders (common causes), the noise dependencies imply further relations between the observed variables. Such models are then closely related…

Accurate prediction of structural dynamics is imperative for preserving digital twin fidelity throughout operational lifetimes. Parametric models with fixed nominal parameters often omit critical physical effects due to simplifications in…

We propose a dynamic factor model (DFM) where the latent factors are linked to observed variables with unknown and potentially nonlinear functions. The key novelty and source of flexibility of our approach is a nonparametric observation…