Related papers: Randomized Physics-Informed Machine Learning for U…

Prevailing machine-learned interatomic potential (MLIP) uncertainty-quantification methods rely on ensembles of independently trained backbones. These methods scale unfavorably with foundation-scale MLIPs, and their member-disagreement…

Large language models (LLMs) demonstrate advanced reasoning abilities, enabling robots to understand natural language instructions and generate high-level plans with appropriate grounding. However, LLM hallucinations present a significant…

In this paper, we consider a Bayesian inverse problem modeled by elliptic partial differential equations (PDEs). Specifically, we propose a data-driven and model-based approach to accelerate the Hamiltonian Monte Carlo (HMC) method in…

Handling incomplete and heterogeneous data remains a central challenge in real-world machine learning, where missing values may follow complex mechanisms (MCAR, MAR, MNAR) and features can be of mixed types (numerical and categorical).…

This work proposes a solution for the problem of training physics-informed networks under partial integro-differential equations. These equations require an infinite or a large number of neural evaluations to construct a single residual for…

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for…

We present a method for computing A-optimal sensor placements for infinite-dimensional Bayesian linear inverse problems governed by PDEs with irreducible model uncertainties. Here, irreducible uncertainties refers to uncertainties in the…

Learning invariant representations is a critical first step in a number of machine learning tasks. A common approach corresponds to the so-called information bottleneck principle in which an application dependent function of mutual…

Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…

A statistical learning approach for parametric PDEs related to Uncertainty Quantification is derived. The method is based on the minimization of an empirical risk on a selected model class and it is shown to be applicable to a broad range…

Aleatoric uncertainty is an intrinsic property of ill-posed inverse and imaging problems. Its quantification is vital for assessing the reliability of relevant point estimates. In this paper, we propose an efficient framework for…

Many Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters that represent the discretization of an underlying function. This work introduces a family of Markov chain Monte Carlo (MCMC)…

Inverse reinforcement learning (IRL) aims to recover the reward function and the associated optimal policy that best fits observed sequences of states and actions implemented by an expert. Many algorithms for IRL have an inherently nested…

Classical penalized likelihood regression problems deal with the case that the independent variables data are known exactly. In practice, however, it is common to observe data with incomplete covariate information. We are concerned with a…

Credal sets, i.e., closed convex sets of probability measures, provide a natural framework to represent aleatoric and epistemic uncertainty in machine learning. Yet how to quantify these two types of uncertainty for a given credal set,…

Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…

Physics-informed extreme learning machines (PIELMs) typically impose boundary and initial conditions through penalty terms, yielding only approximate satisfaction that is sensitive to user-specified weights and can propagate errors into the…

Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…

In an ever-increasing interest for Machine Learning (ML) and a favorable data development context, we here propose an original methodology for data-based prediction of two-dimensional physical fields. Polynomial Chaos Expansion (PCE),…

We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…