A liquid–gas foam, here called bubble array, is a ubiquitous phenomenon widely observed in daily lives, food, pharmaceutical and cosmetic products, and even bio- and nano-technologies. This intriguing phenomenon has been often studied in a well-controlled environment in laboratories, computations, or analytical models. Still, real-world bubble undergoes complex nonlinear transitions from wet to dry conditions, which are hard to describe by unified rules as a whole. Here, we show that a few early-phase snapshots of bubble array can be learned by a glass-box physics rule learner (GPRL) leading to prediction rules of future bubble array. Unlike the black-box machine learning approach, the glass-box approach seeks to unravel expressive rules of the phenomenon that can evolve. Without known principles, GPRL identifies plausible rules of bubble prediction with an elongated bubble array data that transitions from wet to dry states. Then, the best-so-far GPRL-identified rule is applied to an independent circular bubble array, demonstrating the potential generality of the rule. We explain how GPRL uses the spatio-temporal convolved information of early bubbles to mimic the scientist’s perception of bubble sides, shapes, and inter-bubble influences. This research will help combine foam physics and machine learning to better understand and control bubbles.
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. 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. 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. A transparent, flexible link function is proposed as a mathematical expression generator, thereby pursuing “glass-box” prediction. Consistent evolution is realized by integrating a Bayesian update and evolutionary algorithms. The framework is applied to nano-scale contact electrification phenomena, and results show promising performances in unraveling transparent expressions of a hidden physical rule. The proposed approach will catalyze a synergistic machine learning-physics partnership.
more » « less- NSF-PAR ID:
- 10214382
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- Communications Physics
- Volume:
- 3
- Issue:
- 1
- ISSN:
- 2399-3650
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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BACKGROUND Optical sensing devices measure the rich physical properties of an incident light beam, such as its power, polarization state, spectrum, and intensity distribution. Most conventional sensors, such as power meters, polarimeters, spectrometers, and cameras, are monofunctional and bulky. For example, classical Fourier-transform infrared spectrometers and polarimeters, which characterize the optical spectrum in the infrared and the polarization state of light, respectively, can occupy a considerable portion of an optical table. Over the past decade, the development of integrated sensing solutions by using miniaturized devices together with advanced machine-learning algorithms has accelerated rapidly, and optical sensing research has evolved into a highly interdisciplinary field that encompasses devices and materials engineering, condensed matter physics, and machine learning. To this end, future optical sensing technologies will benefit from innovations in device architecture, discoveries of new quantum materials, demonstrations of previously uncharacterized optical and optoelectronic phenomena, and rapid advances in the development of tailored machine-learning algorithms. ADVANCES Recently, a number of sensing and imaging demonstrations have emerged that differ substantially from conventional sensing schemes in the way that optical information is detected. A typical example is computational spectroscopy. In this new paradigm, a compact spectrometer first collectively captures the comprehensive spectral information of an incident light beam using multiple elements or a single element under different operational states and generates a high-dimensional photoresponse vector. An advanced algorithm then interprets the vector to achieve reconstruction of the spectrum. This scheme shifts the physical complexity of conventional grating- or interference-based spectrometers to computation. Moreover, many of the recent developments go well beyond optical spectroscopy, and we discuss them within a common framework, dubbed “geometric deep optical sensing.” The term “geometric” is intended to emphasize that in this sensing scheme, the physical properties of an unknown light beam and the corresponding photoresponses can be regarded as points in two respective high-dimensional vector spaces and that the sensing process can be considered to be a mapping from one vector space to the other. The mapping can be linear, nonlinear, or highly entangled; for the latter two cases, deep artificial neural networks represent a natural choice for the encoding and/or decoding processes, from which the term “deep” is derived. 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INTRODUCTION Solving quantum many-body problems, such as finding ground states of quantum systems, has far-reaching consequences for physics, materials science, and chemistry. Classical computers have facilitated many profound advances in science and technology, but they often struggle to solve such problems. Scalable, fault-tolerant quantum computers will be able to solve a broad array of quantum problems but are unlikely to be available for years to come. Meanwhile, how can we best exploit our powerful classical computers to advance our understanding of complex quantum systems? Recently, classical machine learning (ML) techniques have been adapted to investigate problems in quantum many-body physics. So far, these approaches are mostly heuristic, reflecting the general paucity of rigorous theory in ML. 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Specifically, our classical ML algorithm predicts expectation values of products of local observables in the ground state, with a small error when averaged over the value of x . The run time of the algorithm and the amount of training data required both scale polynomially in m and linearly in the size of the quantum system. Our proof of this result builds on recent developments in quantum information theory, computational learning theory, and condensed matter theory. Furthermore, under the widely accepted conjecture that nondeterministic polynomial-time (NP)–complete problems cannot be solved in randomized polynomial time, we prove that no polynomial-time classical algorithm that does not learn from data can match the prediction performance achieved by the ML algorithm. In a related contribution using similar proof techniques, we show that classical ML algorithms can efficiently learn how to classify quantum phases of matter. In this scenario, the training data consist of classical representations of quantum states, where each state carries a label indicating whether it belongs to phase A or phase B . The ML algorithm then predicts the phase label for quantum states that were not encountered during training. The classical ML algorithm not only classifies phases accurately, but also constructs an explicit classifying function. Numerical experiments verify that our proposed ML algorithms work well in a variety of scenarios, including Rydberg atom systems, two-dimensional random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases. CONCLUSION We have rigorously established that classical ML algorithms, informed by data collected in physical experiments, can effectively address some quantum many-body problems. 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