Related papers: Data-Driven Stochastic Closure Modeling via Condit…

We propose a latent score-based generative AI framework for learning stochastic, non-local closure models and constitutive laws in nonlinear dynamical systems of computational mechanics. This work addresses a key challenge of modeling…

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…

Derivation of reduced order representations of dynamical systems requires the modeling of the truncated dynamics on the retained dynamics. In its most general form, this so-called closure model has to account for memory effects. In this…

We propose a statistical-stochastic surrogate modeling approach to predict the response of the mean and variance statistics under various initial conditions and external forcing perturbations. The proposed modeling framework extends the…

A framework for deriving probabilistic data-driven closure models is proposed for coarse-grained numerical simulations of turbulence in statistically stationary state. The approach unites the ideal large-eddy simulation model and data…

Data-driven modeling techniques have been explored in the spatial-temporal modeling of complex dynamical systems for many engineering applications. However, a systematic approach is still lacking to leverage the information from different…

This short note proposes a model-driven conditional Fourier neural operator (MD-CFNO) for synthetic turbulence generation. Spectrum-consistent synthetic turbulence is essential for inflow boundary construction in computational fluid…

In this paper we develop a new data-driven closure approximation method to compute the statistical properties of quantities of interest in high-dimensional stochastic dynamical systems. The new method relies on estimating conditional…

Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…

Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary…

Model-free data-driven computational mechanics replaces phenomenological constitutive functions by numerical simulations based on data sets of representative samples in stress-strain space. The distance of strain and stress pairs from the…

Complex dynamical systems are used for predictions in many domains. Because of computational costs, models are truncated, coarsened, or aggregated. As the neglected and unresolved terms become important, the utility of model predictions…

Simulating turbulent fluid flows is a computationally prohibitive task, as it requires the resolution of fine-scale structures and the capture of complex nonlinear interactions across multiple scales. This is particularly the case in direct…

We present a novel simulation-free framework for training continuous-time diffusion processes over very general objective functions. Existing methods typically involve either prescribing the optimal diffusion process -- which only works for…

This paper has two interrelated foci: (i) obtaining stable and efficient data-driven closure models by using a multivariate time series of partial observations from a large-dimensional system; and (ii) comparing these closure models with…

Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear…

This study introduces a training-free conditional diffusion model for learning unknown stochastic differential equations (SDEs) using data. The proposed approach addresses key challenges in computational efficiency and accuracy for modeling…

Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…

Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…

Traditional deterministic subgrid-scale (SGS) models are often dissipative and unstable, especially in regions of chaotic and turbulent flow. Ongoing work in climate science and ocean modeling motivates the use of stochastic SGS models for…