Related papers: FUSE: Fast Unified Simulation and Estimation for P…
Partial differential equations (PDEs) govern a wide range of physical phenomena, but their numerical solution remains computationally demanding, especially when repeated simulations are required across many parameter settings. Recent…
We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…
This is the second part of four series papers, aiming at the problem of sensor dynamics compensation for abstract linear systems. Two major issues are addressed. The first one is about the sensor dynamics compensation in system observation…
Ordinary differential equations (ODEs) are central to scientific modelling, but inferring their vector fields from noisy trajectories remains challenging. Current approaches such as symbolic regression, Gaussian process (GP) regression, and…
This paper addresses Bayesian inference related to partial differential equations (PDEs), particularly nonparametric regression constrained by PDEs. To effectively encode prior information, we propose a novel framework that learns a…
Vertical equilibrium (VE) models have been introduced as computationally efficient alternatives to traditional mass and momentum balance equations for fluid flow in porous media. Since VE models are only accurate in regions where phase…
The advancement of human healthspan and bioengineering relies heavily on predicting the behavior of complex biological systems. While high-throughput multiomics data is becoming increasingly abundant, converting this data into actionable…
Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…
The field of numerical simulation is of significant importance for the design and management of real-world systems, with partial differential equations (PDEs) being a commonly used mathematical modeling tool. However, solving PDEs remains…
Hemodynamic parameters such as pressure and wall shear stress play an important role in diagnosis, prognosis, and treatment planning in cardiovascular diseases. These parameters can be accurately computed using computational fluid dynamics…
We propose a predictor-corrector adaptive method for the study of hyperbolic partial differential equations (PDEs) under uncertainty. Constructed around the framework of stochastic finite volume (SFV) methods, our approach circumvents…
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…
We establish oracle inequalities for a version of the Lasso in high-dimensional fixed effects dynamic panel data models. The inequalities are valid for the coefficients of the dynamic and exogenous regressors. Separate oracle inequalities…
In recent years, computational power and data availability breakthroughs have revolutionized our ability to analyze complex physical systems through the inverse problem approach. Data-driven techniques like system identification and machine…
Complex systems are often decomposed into modular subsystems for engineering tractability. Although various equation based white-box modeling techniques make use of such structure, learning based methods have yet to incorporate these ideas…
Industrial design evaluation often relies on high-fidelity simulations of governing partial differential equations (PDEs). While accurate, these simulations are computationally expensive, making dense exploration of design spaces…
Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…
Motivated by the problem of discrete-parameter simulation optimization (DPSO) of queueing systems, we consider the problem of embedding the discrete parameter space into a continuous one so that descent-based continuous-space methods could…
We consider the primal and dual forms of the optimality conditions for PDE-contrained optimization problems arising in Data-Driven Computational Mechanics when specialized to the reaction-diffusion context. Starting with the continuous…
Partial differential equations (PDEs) govern nearly every physical process in science and engineering, yet solving them at scale remains prohibitively expensive. Generative AI has transformed language, vision, and protein science, but…