Discovering Causal Relations and Equations from Data

Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws and principles that are invariant, robust and causal explanations of the world has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventional studies in the system under study. With the advent of big data and the use of data-driven methods, causal and equation discovery fields have grown and made progress in computer science, physics, statistics, philosophy, and many applied fields. All these domains are intertwined and can be used to discover causal relations, physical laws, and equations from observational data. This paper reviews the concepts, methods, and relevant works on causal and equation discovery in the broad field of Physics and outlines the most important challenges and promising future lines of research. We also provide a taxonomy for observational causal and equation discovery, point out connections, and showcase a complete set of case studies in Earth and climate sciences, fluid dynamics and mechanics, and the neurosciences. This review demonstrates that discovering fundamental laws and causal relations by observing natural phenomena is being revolutionised with the efficient exploitation of observational data, modern machine learning algorithms and the interaction with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems.Comment: 137 page

Discovering causal relations and equations from data

Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws, and principles that are invariant, robust, and causal has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventions on the system under study. With the advent of big data and data-driven methods, the fields of causal and equation discovery have developed and accelerated progress in computer science, physics, statistics, philosophy, and many applied fields. This paper reviews the concepts, methods, and relevant works on causal and equation discovery in the broad field of physics and outlines the most important challenges and promising future lines of research. We also provide a taxonomy for data-driven causal and equation discovery, point out connections, and showcase comprehensive case studies in Earth and climate sciences, fluid dynamics and mechanics, and the neurosciences. This review demonstrates that discovering fundamental laws and causal relations by observing natural phenomena is revolutionised with the efficient exploitation of observational data and simulations, modern machine learning algorithms and the combination with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems

Physics-Informed Machine Learning of Argon Gas-Driven Melt Pool Dynamics

Melt pool dynamics in metal additive manufacturing (AM) is critical to process stability, microstructure formation, and final properties of the printed materials. Physics-based simulation including computational fluid dynamics (CFD) is the dominant approach to predict melt pool dynamics. However, the physics-based simulation approaches suffer from the inherent issue of very high computational cost. This paper provides a physics-informed machine learning (PIML) method by integrating neural networks with the governing physical laws to predict the melt pool dynamics such as temperature, velocity, and pressure without using any training data on velocity. This approach avoids solving the highly non-linear Navier-Stokes equation numerically, which significantly reduces the computational cost. The difficult-to-determine model constants of the governing equations of the melt pool can also be inferred through data-driven discovery. In addition, the physics-informed neural network (PINN) architecture has been optimized for efficient model training. The data-efficient PINN model is attributed to the soft penalty by incorporating governing partial differential equations (PDEs), initial conditions, and boundary conditions in the PINN model

Data-driven PDE discovery with evolutionary approach

The data-driven models allow one to define the model structure in cases when a priori information is not sufficient to build other types of models. The possible way to obtain physical interpretation is the data-driven differential equation discovery techniques. The existing methods of PDE (partial derivative equations) discovery are bound with the sparse regression. However, sparse regression is restricting the resulting model form, since the terms for PDE are defined before regression. The evolutionary approach described in the article has a symbolic regression as the background instead and thus has fewer restrictions on the PDE form. The evolutionary method of PDE discovery (EPDE) is described and tested on several canonical PDEs. The question of robustness is examined on a noised data example

A cognitive architecture for learning in reactive environments

Previous research in machine learning has viewed the process of empirical discovery as search through a space of 'theoretical' terms. In this paper, we propose a problem space for empirical discovery, specifying six complementary operators for defining new terms that ease the statement of empirical laws. The six types of terms include: numeric attributes (such as PV/T); intrinsic properties (such as mass); composite objects (such as pairs of colliding balls); classes of objects (such as acids and alkalis); composite relations (such as chemical reactions); and classes of relations (such as combustion/oxidation). We review existing machine discovery systems in light of this framework, examining which parts of the problem space were, covered by these systems. Finally, we outline an integrated discovery system (IDS) we are constructing that includes all six of the operators and which should be able to discover a broad range of empirical laws