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A framework is developed based on different uncertainty quantification (UQ) techniques in order to assess validation and verification (V&V) metrics in computational physics problems, in general, and computational fluid dynamics (CFD), in…

Advancements in computational fluid mechanics have largely relied on Newtonian frameworks, particularly through the direct simulation of Navier-Stokes equations. In this work, we propose an alternative computational framework that employs…

In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…

Recent diffusion models have exhibited great potential in generative modeling tasks. Part of their success can be attributed to the ability of training stable on huge sets of paired synthetic data. However, adapting these models to…

Many gradient-based meta-learning methods assume a set of parameters that do not participate in inner-optimization, which can be considered as hyperparameters. Although such hyperparameters can be optimized using the existing gradient-based…

Accurately, efficiently, and stably computing complex fluid flows and their evolution near solid boundaries over long horizons remains challenging. Conventional numerical solvers require fine grids and small time steps to resolve near-wall…

Robust optimization (RO) has emerged as one of the leading paradigms to efficiently model parameter uncertainty. The recent connections between RO and problems in statistics and machine learning domains demand for solving RO problems in…

Parameter inference in ordinary differential equations is an important problem in many applied sciences and in engineering, especially in a data-scarce setting. In this work, we introduce a novel generative modeling approach based on…

Learning expressive probabilistic models correctly describing the data is a ubiquitous problem in machine learning. A popular approach for solving it is mapping the observations into a representation space with a simple joint distribution,…

Calibrating mathematical models of biological processes is essential for achieving predictive accuracy and gaining mechanistic insight. However, this task remains challenging due to limited and noisy data, significant biological…

Reliable inference of system degradation from sensor data is fundamental to condition monitoring and prognostics in mechanical and infrastructural systems. Since degradation is rarely directly observable and measurable, it must be inferred…

Model order reduction provides low-complexity high-fidelity surrogate models that allow rapid and accurate solutions of parametric differential equations. The development of reduced order models for parametric \emph{nonlinear} Hamiltonian…

Out-of-distribution (OOD) detection aims to identify OOD data based on representations extracted from well-trained deep models. However, existing methods largely ignore the reprogramming property of deep models and thus may not fully…

High-resolution precipitation forecasts are crucial for providing accurate weather prediction and supporting effective responses to extreme weather events. Traditional numerical models struggle with stochastic subgrid-scale processes, while…

This paper presents an efficient surrogate modeling strategy for the uncertainty quantification and Bayesian calibration of a hydrological model. In particular, a process-based dynamical urban drainage simulator that predicts the discharge…

This paper presents an adaptive sampling algorithm tailored for the optimization of parametrized dynamical systems using projection-based model order reduction. Unlike classical sampling strategies, this framework does not aim for a small…

Many physical questions in fluid dynamics can be recast in terms of norm constrained optimisation problems; which in-turn, can be further recast as unconstrained problems on spherical manifolds. Due to the nonlinearities of the governing…

Building a representative model of a complex system remains a highly challenging problem. While by now there is basic understanding of most physical domains, model design is often hindered by lack of detail, for example concerning model…

Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering. Traditional stability and receptivity…

Exploring and modeling rain generation mechanism is critical for augmenting paired data to ease training of rainy image processing models. Against this task, this study proposes a novel deep learning based rain generator, which fully takes…