Related papers: Physics-informed Information Field Theory for Mode…

Information geometry provides a tool to systematically investigate parameter sensitivity of the state of a system. If a physical system is described by a linear combination of eigenstates of a complex (that is, non-Hermitian) Hamiltonian,…

This paper focuses on developing a method to obtain an uncertain linear fractional transformation (LFT) system that adequately captures the dynamics of a nonlinear time-invariant system over some desired envelope. First, the nonlinear…

This article introduces an informative goodness-of-fit (iGOF) approach to study multivariate distributions. When the null model is rejected, iGOF allows us to identify the underlying sources of mismodeling and naturally equips practitioners…

Inverse problems involving partial differential equations (PDEs) can be seen as discovering a mapping from measurement data to unknown quantities, often framed within an operator learning approach. However, existing methods typically rely…

As applications of deep learning (DL) continue to seep into critical scientific use-cases, the importance of performing uncertainty quantification (UQ) with DL has become more pressing than ever before. In scientific applications, it is…

Model-based deep learning solutions to inverse problems have attracted increasing attention in recent years as they bridge state-of-the-art numerical performance with interpretability. In addition, the incorporated prior domain knowledge…

The Rapid Iterative FiTting (RIFT) parameter inference algorithm provides a simulation-based inference approach to efficient, highly-parallelized parameter inference for GW sources. Previous editions of RIFT have conservatively optimized…

The use of machine learning in fluid dynamics is becoming more common to expedite the computation when solving forward and inverse problems of partial differential equations. Yet, a notable challenge with existing convolutional neural…

Inverse problems arise almost everywhere in science and engineering where we need to infer on a quantity from indirect observation. The cases of medical, biomedical, and industrial imaging systems are the typical examples. A very high…

Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying it to systems with Hamiltonian dynamics, a problem of predicting the macroscopic…

In this work we propose an extension of physics informed supervised learning strategies to parametric partial differential equations. Indeed, even if the latter are indisputably useful in many applications, they can be computationally…

Multimodal Machine Translation (MMT) has demonstrated the significant help of visual information in machine translation. However, existing MMT methods face challenges in leveraging the modality gap by enforcing rigid visual-linguistic…

Physics-informed machine learning (PIML) integrates mechanistic knowledge, typically in the form of partial differential equations (PDE), into data-driven models. Despite strong empirical performance, its statistical generalisation…

The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior…

Efficiently performing predictive studies of irradiated particle-laden turbulent flows has the potential of providing significant contributions towards better understanding and optimizing, for example, concentrated solar power systems. As…

Uncertainty quantification is a primary challenge for reliable modeling and simulation of complex stochastic dynamics. Such problems are typically plagued with incomplete information that may enter as uncertainty in the model parameters, or…

We present a differentiable soft-body physics simulator that can be composed with neural networks as a differentiable layer. In contrast to other differentiable physics approaches that use explicit forward models to define state…

Variational inference (VI) is a computationally efficient and scalable methodology for approximate Bayesian inference. It strikes a balance between accuracy of uncertainty quantification and practical tractability. It excels at generative…

Large language models are typically post-trained using supervised fine-tuning (SFT) and reinforcement learning (RL), yet effectively unifying efficient knowledge injection with robust generalization remains challenging. In this work, we…

Physics-informed neural networks allow models to be trained by physical laws described by general nonlinear partial differential equations. However, traditional architectures struggle to solve more challenging time-dependent problems due to…