Related papers: BINDy -- Bayesian identification of nonlinear dyna…

This thesis focuses on the discovery of stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) from noisy and discrete time series. A major challenge is selecting the simplest possible correct model…

In this study, we investigate the performance of the sparse identification of nonlinear dynamics (SINDy) algorithm and the neural ordinary differential equations (ODEs) in identification of the underlying mechanisms of open ocean Lagrangian…

High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and…

It is now well established that sparse signal models are well suited to restoration tasks and can effectively be learned from audio, image, and video data. Recent research has been aimed at learning discriminative sparse models instead of…

The sparse modeling is an evident manifestation capturing the parsimony principle just described, and sparse models are widespread in statistics, physics, information sciences, neuroscience, computational mathematics, and so on. In…

The multiscale and turbulent nature of Earth's atmosphere has historically rendered accurate weather modeling a hard problem. Recently, there has been an explosion of interest surrounding data-driven approaches to weather modeling, which in…

The information bottleneck framework provides a systematic approach to learning representations that compress nuisance information in the input and extract semantically meaningful information about predictions. However, the choice of a…

Sparse deep learning aims to address the challenge of huge storage consumption by deep neural networks, and to recover the sparse structure of target functions. Although tremendous empirical successes have been achieved, most sparse deep…

While the uncertainty in generation and demand increases, accurately estimating the dynamic characteristics of power systems becomes crucial for employing the appropriate control actions to maintain their stability. In our previous work, we…

In the context of population dynamics, identifying effective model features, such as fecundity and mortality rates, is generally a complex and computationally intensive process, especially when the dynamics are heterogeneous across the…

Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…

Simulation-based inference (SBI) enables Bayesian analysis when the likelihood is intractable but model simulations are available. Recent advances in statistics and machine learning, including Approximate Bayesian Computation and deep…

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…

The main contribution of this paper is to develop a hierarchical Bayesian formulation of PINNs for linear inverse problems, which is called BPINN-IP. The proposed methodology extends PINN to account for prior knowledge on the nature of the…

We propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential…

This paper addresses the problem of learning dictionaries for multimodal datasets, i.e. datasets collected from multiple data sources. We present an algorithm called multimodal sparse Bayesian dictionary learning (MSBDL). MSBDL leverages…

While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and…

Pretrained diffusion models are effective priors for Bayesian inverse problems, but posterior sampling with these priors is often costly because data-consistency guidance is applied throughout the full reverse trajectory. Existing methods…

The design of informatively rich input signals is essential for accurate system identification, yet classical Fisher-information-based methods are inherently local and often inadequate in the presence of significant model uncertainty and…

Bayesian multidimensional scaling (BMDS) is a probabilistic dimension reduction tool that allows one to model and visualize data consisting of dissimilarities between pairs of objects. Although BMDS has proven useful within, e.g., Bayesian…