Related papers: Experimental Design for Missing Physics
Data-driven modeling and machine learning are widely used to model the behavior of dynamic systems. One application is the residual evaluation of technical systems where model predictions are compared with measurement data to create…
Augmenting mechanistic ordinary differential equation (ODE) models with machine-learnable structures is an novel approach to create highly accurate, low-dimensional models of engineering systems incorporating both expert knowledge and…
We develop a general approach to distill symbolic representations of a learned deep model by introducing strong inductive biases. We focus on Graph Neural Networks (GNNs). The technique works as follows: we first encourage sparse latent…
Healthcare companies must submit pharmaceutical drugs or medical devices to regulatory bodies before marketing new technology. Regulatory bodies frequently require transparent and interpretable computational modelling to justify a new…
Many promising approaches to symbolic regression have been presented in recent years, yet progress in the field continues to suffer from a lack of uniform, robust, and transparent benchmarking standards. In this paper, we address this…
Modeling complex spatiotemporal dynamics, particularly in far-from-equilibrium systems, remains a grand challenge in science. The governing partial differential equations (PDEs) for these systems are often intractable to derive from first…
The application of machine learning methods to particle physics often doesn't provide enough understanding of the underlying physics. An interpretable model which provides a way to improve our knowledge of the mechanism governing a physical…
Complex dynamic systems are typically either modeled using expert knowledge in the form of differential equations or via data-driven universal approximation models such as artificial neural networks (ANN). While the first approach has…
Despite the growing availability of sensing and data in general, we remain unable to fully characterise many in-service engineering systems and structures from a purely data-driven approach. The vast data and resources available to capture…
Identifying a coupled dynamical system out of many plausible candidates, each of which could serve as the underlying generator of some observed measurements, is a profoundly ill posed problem that commonly arises when modelling real world…
The expansiveness of compositional phase space is too vast to fully search using current theoretical tools for many emergent problems in condensed matter physics. The reliance on a deep chemical understanding is one method to identify local…
Discovering valid and meaningful mathematical equations from observed data plays a crucial role in scientific discovery. While this task, symbolic regression, remains challenging due to the vast search space and the trade-off between…
There is a growing trend in molecular and synthetic biology of using mechanistic (non machine learning) models to design biomolecular networks. Once designed, these networks need to be validated by experimental results to ensure the…
Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…
Inverse problems involving differential equations often require identifying unknown parameters or functions from data. Existing approaches, such as Physics-Informed Neural Networks (PINNs), Universal Differential Equations (UDEs) and…
Neutrino experiments study the least understood of the Standard Model particles by observing their direct interactions with matter or searching for ultra-rare signals. The study of neutrinos typically requires overcoming large backgrounds,…
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…
Symbolic regression (SR) has emerged as a powerful method for uncovering interpretable mathematical relationships from data, offering a novel route to both scientific discovery and efficient empirical modelling. This article introduces the…
Existing methods for structure discovery in time series data construct interpretable, compositional kernels for Gaussian process regression models. While the learned Gaussian process model provides posterior mean and variance estimates,…
Symbolic regression is a powerful tool for knowledge discovery, enabling the extraction of interpretable mathematical expressions directly from data. However, conventional symbolic discovery typically follows an end-to-end, "one-step"…