Related papers: Feature engineering and symbolic regression method…

Machine learning (ML) can facilitate efficient thermoelectric (TE) material discovery essential to address the environmental crisis. However, ML models often suffer from poor experimental generalizability despite high metrics. This study…

Surrogate model can replace the parametric full-order model (FOM) by an approximation model, which can significantly improve the efficiency of optimization design and reduce the complexity of engineering systems. However, due to limitations…

Symbolic regression is a powerful tool for discovering governing equations directly from data, but its sensitivity to noise hinders its broader application. This paper introduces a Sequential Monte Carlo (SMC) framework for Bayesian…

The ``black-box'' nature of deep learning models presents a significant barrier to their adoption for scientific discovery, where interpretability is paramount. This challenge is especially pronounced in discovering the governing equations…

Understanding the decision-making processes of large language models is critical given their widespread applications. To achieve this, we aim to connect a formal mathematical framework - zigzag persistence from topological data analysis -…

Feature selection is a critical component in predictive analytics that significantly affects the prediction accuracy and interpretability of models. Intrinsic methods for feature selection are built directly into model learning, providing a…

Identifying meaningful signal buried in noise is a problem of interest arising in diverse scenarios of data-driven modeling. We present here a theoretical framework for exploiting intrinsic geometry in data that resists noise corruption,…

This article presents an approach for modelling hysteresis in piezoelectric materials, that leverages recent advancements in machine learning, particularly in sparse-regression techniques. While sparse regression has previously been used to…

The statistics of the diffusive motion of particles often serve as an experimental proxy for their interaction with the environment. However, inferring the physical properties from the observed trajectories is challenging. Inspired by a…

In this article we detail the use of machine learning for spatiotemporally dynamic turbulence model classification and hybridization for the large eddy simulations (LES) of turbulence. Our predictive framework is devised around the…

Generative graph models struggle to scale due to the need to predict the existence or type of edges between all node pairs. To address the resulting quadratic complexity, existing scalable models often impose restrictive assumptions such as…

We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setting is notoriously challenging due to the intractability of…

Understanding physical phenomena oftentimes means understanding the underlying dynamical system that governs observational measurements. While accurate prediction can be achieved with black box systems, they often lack interpretability and…

This work presents a data-driven approach to the identification of spatial and temporal truncation errors for linear and nonlinear discretization schemes of Partial Differential Equations (PDEs). Motivated by the central role of truncation…

We present a statistical learning framework for robust identification of partial differential equations from noisy spatiotemporal data. Extending previous sparse regression approaches for inferring PDE models from simulated data, we address…

Neural networks offer highly expressive turbulence closures, yet their complexity obscures the physical mechanisms they aim to model, and their computational cost can limit their tractability. To address these limitations, we introduce a…

Symbolic regression is a technique that can automatically derive analytic models from data. Traditionally, symbolic regression has been implemented primarily through genetic programming that evolves populations of candidate solutions…

Reconstructing PDE solutions from sparse observations is a core challenge in scientific computing. We present FM4PDE, a flow-matching generative framework that learns the joint distribution of PDE coefficients (or initial states) and…

We propose Deep Hierarchical Machine (DHM), a model inspired from the divide-and-conquer strategy while emphasizing representation learning ability and flexibility. A stochastic routing framework as used by recent deep neural…

Feature identification is an important task in many fluid dynamics applications and diverse methods have been developed for this purpose. These methods are based on a physical understanding of the underlying behavior of the flow in the…