Related papers: History-Aware Neural Operator: Robust Data-Driven …

We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…

Recently, neural operators have emerged as powerful tools for learning mappings between function spaces, enabling data-driven simulations of complex dynamics. Despite their successes, a deeper understanding of their learning mechanisms…

Neural operators, which aim to approximate mappings between infinite-dimensional function spaces, have been widely applied in the simulation and prediction of physical systems. However, the limited representational capacity of network…

This paper proposes a supervised machine learning framework for the non-intrusive model order reduction of unsteady fluid flows to provide accurate predictions of non-stationary state variables when the control parameter values vary. Our…

The discovery of constitutive models for hyperelastic materials is essential yet challenging due to their nonlinear behavior and the limited availability of experimental data. Traditional methods typically require extensive stress-strain or…

Learning PDE dynamics from limited data with unknown physics is challenging. Existing neural PDE solvers either require large datasets or rely on known physics (e.g., PDE residuals or handcrafted stencils), leading to limited applicability.…

Visual model-based RL methods typically encode image observations into low-dimensional representations in a manner that does not eliminate redundant information. This leaves them susceptible to spurious variations -- changes in…

Many natural materials exhibit highly complex, nonlinear, anisotropic, and heterogeneous mechanical properties. Recently, it has been demonstrated that data-driven strain energy functions possess the flexibility to capture the behavior of…

Real-world time series data exhibit non-stationary behavior, regime shifts, and temporally varying noise (heteroscedastic) that degrade the robustness of standard regression models. We introduce the Variability-Aware Recursive Neural…

Design and analysis of inelastic materials requires prediction of physical responses that evolve under loading. Numerical simulation of such behavior using finite element (FE) approaches can call for significant time and computational…

Scientific machine learning is increasingly used to build surrogate models, yet most models are trained under a restrictive assumption in which future data follow the same distribution as the training set. In practice, new experimental…

World models learned from high-dimensional visual observations allow agents to make decisions and plan directly in latent space, avoiding pixel-level reconstruction. However, recent latent predictive architectures (JEPAs), including the…

With the advancement of Deep Neural Networks (DNN) and large amounts of sensor data from Internet of Things (IoT) systems, the research community has worked to reduce the computational and resource demands of DNN to compute on low-resourced…

Fourier Neural Operators (FNOs) have demonstrated exceptional accuracy in mapping functional spaces by leveraging Fourier transforms to establish a connection with underlying physical principles. However, their opaque inner workings often…

In visual domain adaptation (DA), separating the domain-specific characteristics from the domain-invariant representations is an ill-posed problem. Existing methods apply different kinds of priors or directly minimize the domain discrepancy…

Numerically solving partial differential equations typically requires fine discretization to resolve necessary spatiotemporal scales, which can be computationally expensive. Recent advances in deep learning have provided a new approach to…

Solving parametric partial differential equations (PDEs) and associated PDE-based, inverse problems is a central task in engineering and physics, yet existing neural operator methods struggle with high-dimensional, discontinuous inputs and…

We propose the geometry-informed neural operator (GINO), a highly efficient approach to learning the solution operator of large-scale partial differential equations with varying geometries. GINO uses a signed distance function and…

Chaos is a fundamental feature of many complex dynamical systems, including weather systems and fluid turbulence. These systems are inherently difficult to predict due to their extreme sensitivity to initial conditions. Many chaotic systems…

The development of data-informed predictive models for dynamical systems is of widespread interest in many disciplines. We present a unifying framework for blending mechanistic and machine-learning approaches to identify dynamical systems…