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Register a new userDiscovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networks
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Sebastian Johann Wetzel
Publication date
2020
fields
Physics
and research's language is
English
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In this paper, we introduce interpretable Siamese Neural Networks (SNN) for similarity detection to the field of theoretical physics. More precisely, we apply SNNs to events in special relativity, the transformation of electromagnetic fields, and the motion of particles in a central potential. In these examples, the SNNs learn to identify datapoints belonging to the same events, field configurations, or trajectory of motion. It turns out that in the process of learning which datapoints belong to the same event or field configuration, these SNNs also learn the relevant symmetry invariants and conserved quantities. These SNNs are highly interpretable, which enables us to reveal the symmetry invariants and conserved quantities without prior knowledge.
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Molecular dynamics is a powerful simulation tool to explore material properties. Most of the realistic material systems are too large to be simulated with first-principles molecular dynamics. Classical molecular dynamics has lower computational cost but requires accurate force fields to achieve chemical accuracy. In this work, we develop a symmetry-adapted graph neural networks framework, named molecular dynamics graph neural networks (MDGNN), to construct force fields automatically for molecular dynamics simulations for both molecules and crystals. This architecture consistently preserves the translation, rotation and permutation invariance in the simulations. We propose a new feature engineering method including higher order contributions and show that MDGNN accurately reproduces the results of both classical and first-principles molecular dynamics. We also demonstrate that force fields constructed by the model has good transferability. Therefore, MDGNN provides an efficient and promising option for molecular dynamics simulations of large scale systems with high accuracy.
When a measurement is made on a system that is not in an eigenstate of the measured observable, it is often assumed that some conservation law has been violated. Discussions of the effect of measurements on conserved quantities often overlook the possibility of entanglement between the measured system and the preparation apparatus. The preparation of a system in any particular state necessarily involves interaction between the apparatus and the system. Since entanglement is a generic result of interaction, as shown by Gemmer and Mahler[1], and by Durt[2,3] one would expect some nonzero entanglement between apparatus and measured system, even though the amount of such entanglement is extremely small. Because the apparatus has an enormous number of degrees of freedom relative to the measured system, even a very tiny difference between the apparatus states that are correlated with the orthogonal states of the measured system can be sufficient to account for the perceived deviation from strict conservation of the quantity in question. Hence measurements need not violate conservation laws.
Machine learning has demonstrated great power in materials design, discovery, and property prediction. However, despite the success of machine learning in predicting discrete properties, challenges remain for continuous property prediction. The challenge is aggravated in crystalline solids due to crystallographic symmetry considerations and data scarcity. Here we demonstrate the direct prediction of phonon density of states using only atomic species and positions as input. We apply Euclidean neural networks, which by construction are equivariant to 3D rotations, translations, and inversion and thereby capture full crystal symmetry, and achieve high-quality prediction using a small training set of $sim 10^{3}$ examples with over 64 atom types. Our predictive model reproduces key features of experimental data and even generalizes to materials with unseen elements,and is naturally suited to efficiently predict alloy systems without additional computational cost. We demonstrate the potential of our network by predicting a broad number of high phononic specific heat capacity materials. Our work indicates an efficient approach to explore materials phonon structure, and can further enable rapid screening for high-performance thermal storage materials and phonon-mediated superconductors.
Finding the precise location of quantum critical points is of particular importance to characterise quantum many-body systems at zero temperature. However, quantum many-body systems are notoriously hard to study because the dimension of their Hilbert space increases exponentially with their size. Recently, machine learning tools known as neural-network quantum states have been shown to effectively and efficiently simulate quantum many-body systems. We present an approach to finding the quantum critical points of the quantum Ising model using neural-network quantum states, analytically constructed innate restricted Boltzmann machines, transfer learning and unsupervised learning. We validate the approach and evaluate its efficiency and effectiveness in comparison with other traditional approaches.
Conserved quantities are crucial in quantum physics. Here we discuss a general scenario of Hamiltonians. All the Hamiltonians within this scenario share a common conserved quantity form. For unitary parametrization processes, the characteristic operator of this scenario is analytically provided, as well as the corresponding quantum Fisher information (QFI). As the application of this scenario, we focus on two classes of Hamiltonians: su(2) category and canonical category. Several specific physical systems in these two categories are discussed in detail. Besides, we also calculate an alternative form of QFI in this scenario.
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