Related papers: From Basis to Basis: Gaussian Particle Representat…
Learning-based simulators show great potential for simulating particle dynamics when 3D groundtruth is available, but per-particle correspondences are not always accessible. The development of neural rendering presents a new solution to…
This paper investigates Gaussian Markov random field approximations to nonstationary Gaussian fields using graph representations of stochastic partial differential equations. We establish approximation error guarantees building on the…
Particle-based representations of radiance fields such as 3D Gaussian Splatting have found great success for reconstructing and re-rendering of complex scenes. Most existing methods render particles via rasterization, projecting them to…
We present an operator learning framework for solving non-perturbative functional renormalization group equations, which are integro-differential equations defined on functionals. Our proposed approach uses Gaussian process operator…
Gaussian scale spaces are a cornerstone of signal representation and processing, with applications in filtering, multiscale analysis, anti-aliasing, and many more. However, obtaining such a scale space is costly and cumbersome, in…
This work is concerned with a simple model for a polar fluid, a Gaussian field model based on the excess density and on the polarization. It is a convenient framework to implement the dielectric properties of correlated liquids that stem…
3D Gaussian Splatting (3DGS) has revolutionized 3D scene representation with superior efficiency and quality. While recent adaptations for computed tomography (CT) show promise, they struggle with severe artifacts under highly sparse-view…
Gaussian states, operations, and measurements are central building blocks for continuous-variable quantum information processing which paves the way for abundant applications, especially including network-based quantum computation and…
Operator learning focuses on approximating mappings $\mathcal{G}^\dagger:\mathcal{U} \rightarrow\mathcal{V}$ between infinite-dimensional spaces of functions, such as $u: \Omega_u\rightarrow\mathbb{R}$ and $v:…
Gaussian process state-space models (GP-SSMs) are a very flexible family of models of nonlinear dynamical systems. They comprise a Bayesian nonparametric representation of the dynamics of the system and additional (hyper-)parameters…
Computational Fluid Dynamics (CFD) plays a pivotal role in fluid mechanics, enabling precise simulations of fluid behavior through partial differential equations (PDEs). However, traditional CFD methods are resource-intensive, particularly…
Global sensitivity analysis of complex numerical simulators is often limited by the small number of model evaluations that can be afforded. In such settings, surrogate models built from a limited set of simulations can substantially reduce…
Real-life control tasks involve matters of various substances---rigid or soft bodies, liquid, gas---each with distinct physical behaviors. This poses challenges to traditional rigid-body physics engines. Particle-based simulators have been…
The success of vision transformers-especially for generative modeling-is limited by the quadratic cost and weak spatial inductive bias of self-attention. We propose PDE-SSM, a spatial state-space block that replaces attention with a…
In recent years, molecular dynamics (MD) simulations have emerged as a pivotal tool for understanding the structure, dynamics, and phase behavior in charged soft matter systems. To explore phenomena across greater length and time scales in…
We present Mechanistic PDE Networks -- a model for discovery of governing partial differential equations from data. Mechanistic PDE Networks represent spatiotemporal data as space-time dependent linear partial differential equations in…
Many modern data sets are sampled with error from complex high-dimensional surfaces. Methods such as tensor product splines or Gaussian processes are effective/well suited for characterizing a surface in two or three dimensions but may…
This paper introduces an innovative approach for representing Gaussian fermionic states, pivotal in quantum spin systems and fermionic models, within a range of alternative quantum bases. We focus on transitioning these states from the…
Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…
Numerically solving partial differential equations (PDEs) can be challenging and computationally expensive. This has led to the development of reduced-order models (ROMs) that are accurate but faster than full order models (FOMs). Recently,…