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Nonlinear reaction-diffusion systems admit a wide variety of spatiotemporal patterns or structures. In this lecture, we point out that there is certain advantage in studying discrete arrays, namely cellular neural/nonlinear networks (CNNs),…
The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and non-diagonal elements of the Fock state. The diagonal elements of the Fock state are solvable but can contain the information about coupling constants.…
Recently, generative machine-learning models have gained popularity in physics, driven by the goal of improving the efficiency of Markov chain Monte Carlo techniques and of exploring their potential in capturing experimental data…
Generative adversarial networks (GANs) are effective in generating realistic images but the training is often unstable. There are existing efforts that model the training dynamics of GANs in the parameter space but the analysis cannot…
Emulate the gating mechanism of ionic channels in neurons, we present a mathematical model for the time constant of dynamical systems. Our model is an analytical continues function. The analyses give evidence that one can adjust the…
Distributed Acoustic Sensing (DAS) is promising for traffic monitoring, but its extensive data and sensitivity to vibrations, causing noise, pose computational challenges. To address this, we propose a two-step deep-learning workflow with…
Generative adversarial nets (GANs) are a promising technique for modeling a distribution from samples. It is however well known that GAN training suffers from instability due to the nature of its maximin formulation. In this paper, we…
We develop a systematic projection-operator technique for constructing Gaussian approximations and their perturbative corrections in bosonic nonlinear models. As a case study, we apply it to the driven dissipative Kerr oscillator. In the…
In active Brownian motion, an internal propulsion mechanism interacts with translational and rotational thermal noise and other internal fluctuations to produce directed motion. We derive the distribution of its extreme fluctuations and…
Latent dynamics discovery is challenging in extracting complex dynamics from high-dimensional noisy neural data. Many dimensionality reduction methods have been widely adopted to extract low-dimensional, smooth and time-evolving latent…
2D convolutional neural networks (CNNs) have attracted significant attention for hyperspectral image super-resolution tasks. However, a key limitation is their reliance on local neighborhoods, which leads to a lack of global contextual…
Time-dependent perturbations can drive a trivial two-dimensional band insulator into a quantum Hall-like phase, with protected nonequilibrium states bound to its edges. We propose an experiment to probe the existence of these topological…
Attractors of dynamical systems may be networks in phase space that can be heteroclinic (where there are dynamical connections between simple invariant sets) or excitable (where a perturbation threshold needs to be crossed to a dynamical…
We have investigated the electrostatics and electronic transport of the gate tunable 2D pn junction by implementing a comprehensive physics-based simulator that self-consistently solves the 2D Poisson's equation coupled to the…
The brain's Path Integration (PI) mechanism offers substantial guidance and inspiration for Brain-Inspired Navigation (BIN). However, the PI capability constructed by the Continuous Attractor Neural Networks (CANNs) in most existing BIN…
We present a data-driven framework for the multiscale modeling of anisotropic finite strain elasticity based on physics-augmented neural networks (PANNs). Our approach allows the efficient simulation of materials with complex underlying…
We extend and improve the work of Model Agnostic Anchors for explanations on image classification through the use of generative adversarial networks (GANs). Using GANs, we generate samples from a more realistic perturbation distribution, by…
Linear-Nonlinear-Poisson (LNP) models are a popular and powerful tool for describing encoding (stimulus-response) transformations by single sensory as well as motor neurons. Recently, there has been rising interest in the second- and…
To gain insight into the neural events responsible for visual perception of static and dynamic optical patterns, we study how neural activation spreads in arrays of inhibition-stabilized neural networks with nearest-neighbor coupling. The…
A generative model with a disentangled representation allows for independent control over different aspects of the output. Learning disentangled representations has been a recent topic of great interest, but it remains poorly understood. We…