In particular, we propose a framework that can facilely deal with multifaceted measurements of 3D specimens by incorporating basic physics and scientists’ experience. This research proposes a framework for a constantly evolving, “glass-box” (as opposed to the black-box) rule learner which can help extract hidden physical rules behind complex real-world phenomena by integrating experienced scientists’ knowledge and the central notions of deep learning. A comparable recent work to our framework would be 15 which pursues both hidden coordinates and a parsimonious form of governing equation of dynamic systems although the key methods and procedures are different. In essence, this framework is purely data-driven, requiring no distributional assumptions about priors and posteriors compared to 14. Last, the identified expressions can easily evolve by embracing other physics and more experience. Third, it is built upon two ingredients, the externalized multi-layer convolved information index and flexible link functions which reinterpret and inherit the deep learning’s successful philosophies. Second, it seeks to leverage basic physics and scientists’ experience rather than relying upon the predefined global governing equations. First, this framework focuses on obtaining transparent expressions of hidden physical rules. Still, this study differs from prior works in several aspects. The present goal of searching hidden rules shares the similar notion with auto-encoder methods in pursuit of salient latent terms 14. Governing physical rules (often partial differential equations) are often fed into ML, e.g., geophysics by an hierarchical graph model 12 and wave and fluid flow by deep learning 13. human neurology 9, quantum mechanics 10, and heterogeneous composite structures 11. Domain science is used to help ML to predict physically sound solutions, e.g. Recently, a new research paradigm emerges to address these hurdles, i.e., the so-called physics- or theory-guided ML paradigm 8. Scientists seek to find “expressions” of physical rules, not merely a “black-box” prediction. The size and volume of physical experimental data are relatively small for direct adoption of advanced ML methods. A few apparent descriptors are insufficient for learning. Physical measurements are often scattered over complex 3D spaces or objects. This fundamental process poses several obstacles to the advanced ML methods. Scientific discovery often follows a typical process-measuring complex physical quantities, investigating the observed data, and deriving a rule that best describes the target physical phenomenon. A direct adoption of an advanced ML method can hardly guarantee successful learning and prediction of the real-world experimental data that often involve 3D objects and multifaceted physical measurements. Often, successful ML methods are limited to opaque decision-making capability about simple tasks. Although advanced machine learning (ML) methods gradually master and replace the complex actions that require the human-level intelligence and control capabilities 6, 7, there exists a deep chasm between advanced ML methods and mature areas of science and engineering. But, the extension of deep learning to three-dimensional (3D) data sets is an active research area facing many theoretical and computational challenges 4, 5. We have seen many triumphs of deep learning architectures successfully working on two-dimensional (2D) data sets, e.g. The proposed approach will catalyze a synergistic machine learning-physics partnership. The framework is applied to nano-scale contact electrification phenomena, and results show promising performances in unraveling transparent expressions of a hidden physical rule. Consistent evolution is realized by integrating a Bayesian update and evolutionary algorithms. A transparent, flexible link function is proposed as a mathematical expression generator, thereby pursuing “glass-box” prediction. A “convolved information index” is proposed to handle physical measurements over three-dimensional nano-scale specimens, and the multi-layered convolutions are “externalized” over multiple depths at the information level, not in the opaque networks. Here we propose a framework that can infuse scientists’ basic knowledge into a glass-box rule learner to extract hidden physical rules behind complex physics phenomena. Attempts to use machine learning to discover hidden physical rules are in their infancy, and such attempts confront more challenges when experiments involve multifaceted measurements over three-dimensional objects.
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