Related papers: Discovery of physically interpretable wave equatio…
Despite the fact that our physical observations can often be described by derived physical laws, such as the wave equation, in many cases, we observe data that do not match the laws or have not been described physically yet. Therefore…
Machine learning offers an intriguing alternative to first-principles analysis for discovering new physics from experimental data. However, to date, purely data-driven methods have only proven successful in uncovering physical laws…
Discovering interpretable physical laws from high-dimensional data is a fundamental challenge in scientific research. Traditional methods, such as symbolic regression, often produce complex, unphysical formulas when searching a vast space…
Many supervised machine learning methods have revolutionised the empirical modelling of complex systems. These empirical models, however, are usually "black boxes" and provide only limited physical explanations about the underlying systems.…
Big data and large-scale machine learning have had a profound impact on science and engineering, particularly in fields focused on forecasting and prediction. Yet, it is still not clear how we can use the superior pattern matching abilities…
In scientific machine learning, the task of identifying partial differential equations accurately from sparse and noisy data poses a significant challenge. Current sparse regression methods may identify inaccurate equations on sparse and…
Automated scientific discovery aims to improve scientific understanding through machine learning. A central approach in this field is symbolic regression, which uses genetic programming or sparse regression to learn interpretable…
Discovering symbolic differential equations from data uncovers fundamental dynamical laws underlying complex systems. However, existing methods often struggle with the vast search space of equations and may produce equations that violate…
Analog machine learning hardware platforms promise to be faster and more energy-efficient than their digital counterparts. Wave physics, as found in acoustics and optics, is a natural candidate for building analog processors for…
Simulating and predicting dynamics of quantum many-body systems is extremely challenging, even for state-of-the-art computational methods, due to the spread of entanglement across the system. However, in the long-wavelength limit, quantum…
Gravitational-wave data analysis is rapidly absorbing techniques from deep learning, with a focus on convolutional networks and related methods that treat noisy time series as images. We pursue an alternative approach, in which waveforms…
Certain neural network architectures, in the infinite-layer limit, lead to systems of nonlinear differential equations. Motivated by this idea, we develop a framework for analyzing time signals based on non-autonomous dynamical equations.…
A second generation of gravitational wave detectors will soon come online with the objective of measuring for the first time the tiny gravitational signal from the coalescence of black hole and/or neutron star binaries. In this…
We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity promoting…
A complete understanding of physical systems requires models that are accurate and obeys natural conservation laws. Recent trends in representation learning involve learning Lagrangian from data rather than the direct discovery of governing…
Controlling systems governed by partial differential equations is an inherently hard problem. Specifically, control of wave dynamics is challenging due to additional physical constraints and intrinsic properties of wave phenomena such as…
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…
Conservation laws are an inherent feature in many systems modeling real world phenomena, in particular, those modeling biological and chemical systems. If the form of the underlying dynamical system is known, linear algebra and algebraic…
The modern machine learning methods allow one to obtain the data-driven models in various ways. However, the more complex the model is, the harder it is to interpret. In the paper, we describe the algorithm for the mathematical equations…
The automated discovery of constitutive laws forms an emerging research area, that focuses on automatically obtaining symbolic expressions describing the constitutive behavior of solid materials from experimental data. Existing…