Related papers: Towards Generalizable PDE Dynamics Forecasting via…

Climate and weather prediction traditionally relies on complex numerical simulations of atmospheric physics. Deep learning approaches, such as transformers, have recently challenged the simulation paradigm with complex network forecasts.…

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…

Partial differential equations (PDEs) play a central role in describing many physical phenomena. Various scientific and engineering applications demand a versatile and differentiable PDE solver that can quickly generate solutions with…

Invariant learning methods, aimed at identifying a consistent predictor across multiple environments, are gaining prominence in out-of-distribution (OOD) generalization. Yet, when environments aren't inherent in the data, practitioners must…

Air pollution significantly threatens human health and ecosystems, necessitating effective air quality prediction to inform public policy. Traditional approaches are generally categorized into physics-based and data-driven models.…

Dynamical systems governed by ordinary differential equations (ODEs) serve as models for a vast number of natural and social phenomena. In this work, we offer a fresh perspective on the classical problem of imputing missing time series…

This work aims to improve fuel chamber injectors' performance in turbofan engines, thus implying improved performance and reduction of pollutants. This requires the development of models that allow real-time prediction and improvement of…

Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…

In this work, we introduce implicit Finite Operator Learning (iFOL) for the continuous and parametric solution of partial differential equations (PDEs) on arbitrary geometries. We propose a physics-informed encoder-decoder network to…

Deep learning-based trajectory prediction models for autonomous driving often struggle with generalization to out-of-distribution (OOD) scenarios, sometimes performing worse than simple rule-based models. To address this limitation, we…

We propose a novel fine-tuning method to achieve multi-operator learning through training a distributed neural operator with diverse function data and then zero-shot fine-tuning the neural network using physics-informed losses for…

Machine learned partial differential equation (PDE) solvers trade the reliability of standard numerical methods for potential gains in accuracy and/or speed. The only way for a solver to guarantee that it outputs the exact solution is to…

Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…

Diffusion models have recently emerged as powerful stochastic frameworks for high-dimensional inference and generation. However, existing applications to partial differential equations (PDEs) predominantly rely on physics-informed training…

Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of…

Unveiling the underlying governing equations of nonlinear dynamic systems remains a significant challenge. Insufficient prior knowledge hinders the determination of an accurate candidate library, while noisy observations lead to imprecise…

Manifold-learning techniques are routinely used in mining complex spatiotemporal data to extract useful, parsimonious data representations/parametrizations; these are, in turn, useful in nonlinear model identification tasks. We focus here…

Forecasting high-dimensional dynamical systems is a fundamental challenge in various fields, such as geosciences and engineering. Neural Ordinary Differential Equations (NODEs), which combine the power of neural networks and numerical…

In scientific and engineering applications, solving partial differential equations (PDEs) across various parameters and domains normally relies on resource-intensive numerical methods. Neural operators based on deep learning offered a…

Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution.…