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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…
The ability to discover physical laws and governing equations from data is one of humankind's greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development…
The fundamental laws of physics are intrinsically geometric, dictating the evolution of systems through principles of symmetry and conservation. While modern machine learning offers powerful tools for modeling complex dynamics from data,…
Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…
Gravitational wave astronomy has emerged as a new branch of observational astronomy, since the first detection of gravitational waves in 2015. The current number of $O(100)$ detections is expected to grow by several orders of magnitude over…
Discovering governing equations of complex network dynamics is a fundamental challenge in contemporary science with rich data, which can uncover the mysterious patterns and mechanisms of the formation and evolution of complex phenomena in…
Humans gain an implicit understanding of physical laws through observing and interacting with the world. Endowing an autonomous agent with an understanding of physical laws through experience and observation is seldom practical: we should…
Most common mechanistic models are traditionally presented in mathematical forms to explain a given physical phenomenon. Machine learning algorithms, on the other hand, provide a mechanism to map the input data to output without explicitly…
The use of machine learning to estimate the energy of a group of atoms, and the forces that drive them to more stable configurations, has revolutionized the fields of computational chemistry and materials discovery. In this domain, rigorous…
The scientific study of the Solar System's minor bodies ultimately starts with a search for those bodies. This chapter presents a review of the use of machine learning techniques to find moving objects, both natural and artificial, in…
Machine learning is playing an increasing role in the physical sciences and significant progress has been made towards embedding domain knowledge into models. Less explored is its use to discover interpretable physical laws from data. We…
The gravity model, inspired by Newton's law of universal gravitation, has long served as a primary tool for interpreting trade flows between countries, using a country's economic `mass' as a key determinant. Despite its wide application,…
Understanding complex systems with their reduced model is one of the central roles in scientific activities. Although physics has greatly been developed with the physical insights of physicists, it is sometimes challenging to build a…
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…
Discovering governing equations from data is crucial for understanding complex systems in many diverse fields from science to engineering. Yet, there still is a lack of versatile computational toolbox to deal with this long standing…
Machine learning is a novel and powerful technology and has been widely used in various science topics. We demonstrate a machine-learning based approach built by a set of general metrics and rules inspired by physics. Taking advantages of…
In an earlier work by a subset of the present authors, the method of the so-called neural deflation was introduced towards identifying a complete set of functionally independent conservation laws of a nonlinear dynamical system. Here, we…
Energy conservation is a basic physics principle, the breakdown of which often implies new physics. This paper presents a method for data-driven "new physics" discovery. Specifically, given a trajectory governed by unknown forces, our…
Galactic rotation curves are crucial for understanding the distribution of mass in galaxies. Despite advances in precision observations, there are discrepancies between the inferred mass from luminosity and the observed rotational…
The beauty of physics is that there is usually a conserved quantity in an always-changing system, known as the constant of motion. Finding the constant of motion is important in understanding the dynamics of the system, but typically…