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The integration of artificial intelligence (AI) into fundamental science has opened new possibilities to address long-standing scientific challenges rooted in mathematical limitations. For example, topological invariants are used to…

Topological phase transitions, which do not adhere to Landau's phenomenological model (i.e. a spontaneous symmetry breaking process and vanishing local order parameters) have been actively researched in condensed matter physics. Machine…

Recently, a new frontier in computing has emerged with physical neural networks(PNNs) harnessing intrinsic physical processes for learning. Here, we explore topological mechanical neural networks(TMNNs) inspired by the quantum spin Hall…

Machine learning has revolutionized the high-dimensional representations for molecular properties such as potential energy. However, there are scarce machine learning models targeting tensorial properties, which are rotationally covariant.…

We introduce an approach for imposing physically informed inductive biases in learned simulation models. We combine graph networks with a differentiable ordinary differential equation integrator as a mechanism for predicting future states,…

A number of machine learning tasks entail a high degree of invariance: the data distribution does not change if we act on the data with a certain group of transformations. For instance, labels of images are invariant under translations of…

Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved throughout the evolution. Physics Informed Neural Networks and…

Deep Neural Networks have shown promising classification performance when predicting certain biomarkers from Whole Slide Images in digital pathology. However, the calibration of the networks' output probabilities is often not evaluated.…

Drawing the quantum phase diagram of a many-body system in the parameter space of its Hamiltonian can be seen as a learning problem, which implies labelling the corresponding ground states according to some classification criterium that…

Functional brain networks exhibit topological structures that reflect neural organization; however, statistical comparison of these networks is challenging for several reasons. This paper introduces a topologically invariant permutation…

Hamiltonian parameter estimation is crucial in condensed matter physics, but time and cost consuming in terms of resources used. With advances in observation techniques, high-resolution images with more detailed information are obtained,…

Learning quantum Hamiltonians with high precision is important for quantum physics and quantum information science. We propose a multi-stage neural network framework that significantly enhances Hamiltonian learning precision through…

Learning workable representations of dynamical systems is becoming an increasingly important problem in a number of application areas. By leveraging recent work connecting deep neural networks to systems of differential equations, we…

We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed…

Using transformers over large generated datasets, we train models to learn mathematical properties of differential systems, such as local stability, behavior at infinity and controllability. We achieve near perfect prediction of qualitative…

After decades of progress and effort, obtaining a phase diagram for a strongly-correlated topological system still remains a challenge. Although in principle one could turn to Wilson loops and long-range entanglement, evaluating these…

Complex prediction models such as deep learning are the output from fitting machine learning, neural networks, or AI models to a set of training data. These are now standard tools in science. A key challenge with the current generation of…

We show that the bulk winding number characterizing one-dimensional topological insulators with chiral symmetry can be detected from the displacement of a single particle, observed via losses. Losses represent the effect of repeated weak…

The past few years have witnessed an increased interest in learning Hamiltonian dynamics in deep learning frameworks. As an inductive bias based on physical laws, Hamiltonian dynamics endow neural networks with accurate long-term…

We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped"…