Related papers: Breaking the Discretization Barrier of Continuous …
Model-based control faces fundamental challenges in partially-observable environments due to unmodeled obstacles. We propose an online learning and optimization method to identify and avoid unobserved obstacles online. Our method,…
We study a class of dynamical networks modeled by linear and time-invariant systems which are described by state-space realizations. For these networks, we investigate the relations between various types of factorizations which preserve the…
I introduce an innovative methodology for deriving numerical models of systems of partial differential equations which exhibit the evolution of spatial patterns. The new approach directly produces a discretisation for the evolution of the…
We propose a computer-assisted approach to studying the effective continuum behavior of spatially discrete evolution equations. The advantage of the approach is that the "coarse model" (the continuum, effective equation) need not be…
Understanding sequential information is a fundamental task for artificial intelligence. Current neural networks attempt to learn spatial and temporal information as a whole, limited their abilities to represent large scale spatial…
Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…
The rapid evolution of Cyber-Physical Systems (CPS) across various domains like mobility systems, networked control systems, sustainable manufacturing, smart power grids, and the Internet of Things necessitates innovative solutions that…
Many learning problems require predicting sets of objects when the number of objects is not known beforehand. Examples include object detection, molecular modeling, and scientific inference tasks such as astrophysical source detection.…
Simulations of complex physical systems are typically realized by discretizing partial differential equations (PDEs) on unstructured meshes. While neural networks have recently been explored for surrogate and reduced order modeling of PDE…
A recurrent task in coordinated systems is managing (estimating, predicting, or controlling) signals that vary in space, such as distributed sensed data or computation outcomes. Especially in large-scale settings, the problem can be…
We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation…
This paper proposes a physical-statistical modeling approach for spatio-temporal data arising from a class of stochastic convection-diffusion processes. Such processes are widely found in scientific and engineering applications where…
Cyber-physical systems (CPS) are increasingly becoming driven by data, using multiple types of sensors to capture huge amounts of data. Extraction and characterization of useful information from big streams of data is a challenging problem.…
Accurate representation of interfaces and flux exchange is vital for coupled multiphysics simulations across a broad range of applications. Currently, coupling approaches are limited by the underlying discretization or to specific physical…
Extreme environmental events frequently exhibit spatial and temporal dependence. These data are often modeled using max stable processes (MSPs). MSPs are computationally prohibitive to fit for as few as a dozen observations, with supposed…
In this work, we consider alternative discretizations for PDEs which use expansions involving integral operators to approximate spatial derivatives. These constructions use explicit information within the integral terms, but treat boundary…
Cyber-physical systems (CPS) encounter a large volume of data which is added to the system gradually in real time and not altogether in advance. As the volume of data increases, the domain of the control strategies also increases, and thus…
Partial differential equations (PDEs) describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated quantities (like entropy). Preserving these conservation and…
Dynamic scene reconstruction from casual videos has seen recent remarkable progress. Numerous approaches have attempted to overcome the ill-posedness of the task by distilling priors from 2D foundational models and by imposing hand-crafted…
We introduce a novel grid-independent model for learning partial differential equations (PDEs) from noisy and partial observations on irregular spatiotemporal grids. We propose a space-time continuous latent neural PDE model with an…