Related papers: Feature engineering and symbolic regression method…
Industrial process monitoring increasingly relies on sensor-generated time-series data, yet the lack of labels, high variability, and operational noise make it difficult to extract meaningful patterns using conventional methods. Existing…
The dynamic model is one of the most successful inventions in subgrid-scale (SGS) modeling as it alleviates many drawbacks of the static coefficient SGS stress models. The model coefficient is often calculated dynamically through the…
Compact symbolic expressions have been shown to be more efficient than neural network models in terms of resource consumption and inference speed when implemented on custom hardware such as FPGAs, while maintaining comparable…
Identification of features is a critical task in microbiome studies that is complicated by the fact that microbial data are high dimensional and heterogeneous. Masked by the complexity of the data, the problem of separating signals from…
The advent of Scientific Machine Learning has heralded a transformative era in scientific discovery, driving progress across diverse domains. Central to this progress is uncovering scientific laws from experimental data through symbolic…
Identifying dynamical system (DS) is a vital task in science and engineering. Traditional methods require numerous calls to the DS solver, rendering likelihood-based or least-squares inference frameworks impractical. For efficient parameter…
Model-based approaches for (bio)process systems often suffer from incomplete knowledge of the underlying physical, chemical, or biological laws. Universal differential equations, which embed neural networks within differential equations,…
In spatially extended systems, it is common to find latent variables that are hard, or even impossible, to measure with acceptable precision, but are crucially important for the proper description of the dynamics. This substantially…
Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is…
In high energy density physics (HEDP) and inertial confinement fusion (ICF), predictive modeling is complicated by uncertainty in parameters that characterize various aspects of the modeled system, such as those characterizing material…
We revisit the Gaussian process model with spherical harmonic features and study connections between the associated RKHS, its eigenstructure and deep models. Based on this, we introduce a new class of kernels which correspond to deep models…
Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift…
A central challenge in materials science is characterizing chemical processes that are elusive to direct measurement, particularly in functional materials operating under realistic conditions. Here, we demonstrate that mechanical strain…
We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…
Symbolic regression is the process of identifying mathematical expressions that fit observed output from a black-box process. It is a discrete optimization problem generally believed to be NP-hard. Prior approaches to solving the problem…
We devise a method to detect and estimate forces in a heterogeneous environment based on experimentally recorded stochastic trajectories. In particular, we focus on systems modeled by the heterogeneous overdamped Langevin equation. Here,…
Modelling complex physical systems through partial differential equations (PDEs) is central to many disciplines in science and engineering. Yet in most real applications, unknown or incomplete relationships such as constitutive or thermal…
Optimization-based problems have become of great interest for signal approximation purposes, as they achieved good accuracy results while being extremely flexible and versatile. In this work, we put our focus on the context of periodic…
Pattern formation is a widely observed phenomenon in diverse fields including materials physics, developmental biology and ecology, among many others. The physics underlying the patterns is specific to the mechanisms, and is encoded by…
We propose a novel differentiable physics engine for system identification of complex spring-rod assemblies. Unlike black-box data-driven methods for learning the evolution of a dynamical system and its parameters, we modularize the design…