Related papers: Minimum Reduced-Order Models via Causal Inference

Thermospheric mass density is a major driver of satellite drag, the largest source of uncertainty in accurately predicting the orbit of satellites in low Earth orbit (LEO) pertinent to space situational awareness. Most existing models for…

Causal and attribution studies are essential for earth scientific discoveries and critical for informing climate, ecology, and water policies. However, the current generation of methods needs to keep pace with the complexity of scientific…

The motivation of this work is an inverse problem for the acoustic wave equation, where an array of sensors probes an unknown medium with pulses and measures the scattered waves. The goal of the inversion is to determine from these…

We present a hybrid constraint-based/Bayesian algorithm for learning causal networks in the presence of sparse data. The algorithm searches the space of equivalence classes of models (essential graphs) using a heuristic based on…

We present a novel reduced order model (ROM) approach for parameterized time-dependent PDEs based on modern learning. The ROM is suitable for multi-query problems and is nonintrusive. It is divided into two distinct stages: A nonlinear…

Model order reduction (MOR) methods that are designed to preserve structural features of a given full order model (FOM) often suffer from a lower accuracy when compared to their non-structure-preserving counterparts. In this paper, we…

Sparse regression has recently emerged as an attractive approach for discovering models of spatiotemporally complex dynamics directly from data. In many instances, such models are in the form of nonlinear partial differential equations…

We consider an optimization problem related to semi-active damping of vibrating systems. The main problem is to determine the best damping matrix able to minimize influence of the input on the output of the system. We use a minimization…

Stochastic reduced-order modeling based on time-dependent bases (TDBs) has proven successful for extracting and exploiting low-dimensional manifold from stochastic partial differential equations (SPDEs). The nominal computational cost of…

Nonlinear aeroelastic reduced-order models (ROMs) based on machine learning or artificial intelligence algorithms can be complex and computationally demanding to train, meaning that for practical aeroelastic applications, the conservative…

Most neural models of causality assume static causal graphs, failing to capture the dynamic and sparse nature of physical interactions where causal relationships emerge and dissolve over time. We introduce the Causal Process Framework and…

This paper aims to propose and theoretically analyze a new distributed scheme for sparse linear regression and feature selection. The primary goal is to learn the few causal features of a high-dimensional dataset based on noisy observations…

Solving complex partial differential equations is vital in the physical sciences, but often requires computationally expensive numerical methods. Reduced-order models (ROMs) address this by exploiting dimensionality reduction to create fast…

We introduce an approach which allows detecting causal relationships between variables for which the time evolution is available. Causality is assessed by a variational scheme based on the Information Imbalance of distance ranks, a…

Reduced order models (ROMs) that capture flow dynamics are of interest for decreasing computational costs for simulation as well as for model-based control approaches. This work presents a data-driven framework for minimal-dimensional…

Structural Causal Models (SCMs) offer a principled framework to reason about interventions and support out-of-distribution generalization, which are key goals in scientific discovery. However, the task of learning SCMs from observed data…

Multiscale dynamical systems characterized by interacting fast and slow processes are ubiquitous across scientific domains, from climate dynamics to fluid mechanics. Accurate modeling of such systems requires capturing both the long-term…

We propose, analyze, and test a novel continuous data assimilation reduced order model (DA-ROM) for simulating incompressible flows. While ROMs have a long history of success on certain problems with recurring dominant structures, they tend…

In this paper, we present a brief tutorial on reduced order model (ROM) closures. First, we carefully motivate the need for ROM closure modeling in under-resolved simulations. Then, we construct step by step the ROM closure model by…

This paper explores how to identify a reduced order model (ROM) from a physical system. A ROM captures an invariant subset of the observed dynamics. We find that there are four ways a physical system can be related to a mathematical model:…