Related papers: Feature engineering and symbolic regression method…

Diffusion has emerged as a powerful framework for generative modeling, achieving remarkable success in applications such as image and audio synthesis. Enlightened by this progress, we propose a novel diffusion-based approach for symbolic…

Learning features from data is one of the defining characteristics of deep learning, but our theoretical understanding of the role features play in deep learning is still rudimentary. To address this gap, we introduce a new tool, the…

We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or…

Recent years have seen substantial advances in the development of biofunctional materials using synthetic polymers. The growing problem of elusive sequence-functionality relations for most biomaterials has driven researchers to seek more…

We introduce DeepMoD, a Deep learning based Model Discovery algorithm. DeepMoD discovers the partial differential equation underlying a spatio-temporal data set using sparse regression on a library of possible functions and their…

Deep generative models such as flow matching and diffusion models have shown great potential in learning complex distributions and dynamical systems, but often act as black-boxes, neglecting underlying physics. In contrast, physics-based…

Discovering hidden physical laws and identifying governing system parameters from sparse observations are central challenges in computational science and engineering. Existing data-driven methods, such as physics-informed neural networks…

In this work we explore the possibility of using sparse statistical modeling in condensed matter physics. The procedure is employed to two well known problems: elemental superconductors and heavy fermions, and was shown that in most cases…

Gaining and understanding the flow dynamics have much importance in a wide range of disciplines, e.g. astrophysics, geophysics, biology, mechanical engineering and biomedical engineering. As a reliable way in practice, especially for…

We present a graph theory-based method to characterise flow defects and structural shifts in condensed matter. We explore the connection between dynamical properties, particularly the recently introduced concept of ''softness'', and…

Sparse regression and feature extraction are the cornerstones of knowledge discovery from massive data. Their goal is to discover interpretable and predictive models that provide simple relationships among scientific variables. While the…

Symbolic regression automates the process of learning closed-form mathematical models from data. Standard approaches to symbolic regression, as well as newer deep learning approaches, rely on heuristic model selection criteria, heuristic…

The random feature method (RFM) has demonstrated great potential in bridging traditional numerical methods and machine learning techniques for solving partial differential equations (PDEs). It retains the advantages of mesh-free approaches…

Regression models usually tend to recover a noisy signal in the form of a combination of regressors, also called features in machine learning, themselves being the result of a learning process.The alignment of the prior covariance feature…

Form a pure mathematical point of view, common functional forms representing different physical phenomena can be defined. For example, rates of chemical reactions, diffusion and heat transfer are all governed by exponential-type…

We introduce SymbolFit, a framework that automates parametric modeling by using symbolic regression to perform a machine-search for functions that fit the data while simultaneously providing uncertainty estimates in a single run.…

We present two approaches to system identification, i.e. the identification of partial differential equations (PDEs) from measurement data. The first is a regression-based Variational System Identification procedure that is advantageous in…

Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…

The sparse representation of signals defined on Euclidean domains has been successfully applied in signal processing. Bringing the power of sparse representations to non-regular domains is still a challenge, but promising approaches have…

Computational Fluid Dynamics (CFD) is an indispensable method of fluid modelling in engineering applications, reducing the need for physical prototypes and testing for tasks such as design optimisation and performance analysis. Depending on…