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Understanding and prediction of the chemical reactions are fundamental demanding in the study of many complex chemical systems. Reactive molecular dynamics (MD) simulation has been widely used for this purpose as it can offer atomic details…
Deep Neural Networks (DNNs) share important similarities with structural glasses. Both have many degrees of freedom, and their dynamics are governed by a high-dimensional, non-convex landscape representing either the loss or energy,…
Capsules are the multidimensional analogue to scalar neurons in neural networks, and because they are multidimensional, much more complex routing schemes can be used to pass information forward through the network than what can be used in…
In this paper, we present a deep neural network based adaptive learning (DNN-AL) approach for switched systems. Currently, deep neural network based methods are actively developed for learning governing equations in unknown dynamic systems,…
Hamiltonian dynamical systems possessing equilibria of ${saddle} \times {centre} \times...\times {centre}$ stability type display \emph{reaction-type dynamics} for energies close to the energy of such equilibria; entrance and exit from…
Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and…
Dynamical systems with complex behaviours, e.g. immune system cells interacting with a pathogen, are commonly modelled by splitting the behaviour into different regimes, or modes, each with simpler dynamics, and then learning the switching…
Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…
This paper proposes a deep learning architecture based on Residual Network that dynamically adjusts the number of executed layers for the regions of the image. This architecture is end-to-end trainable, deterministic and problem-agnostic.…
Using the techniques of Neural Networks (NN), we study the three-dimensional (3D) 5-state ferromagnetic Potts model on the cubic lattice as well as the two-dimensional (2D) 3-state antiferromagnetic Potts model on the square lattice. Unlike…
A new learning scheme called time divergence-convergence (TDC) is proposed for two-layer dynamic synapse neural networks (DSNN). DSNN is an artificial neural network model, in which the synaptic transmission is modeled by a dynamic process…
Dynamical systems describe how a physical system evolves over time. Physical processes can evolve faster or slower in different environmental conditions. We use time-warping as rescaling the time in a model of a physical system. This thesis…
Neural network methods are increasingly applied to solve phase transition problems, particularly in identifying critical points in non-equilibrium phase transitions, offering more convenience compared to traditional methods. In this paper,…
Mathematical modeling has broad applications in neuroscience whether modeling the dynamics of a single synapse or an entire network of neurons. In Part I, we model vesicle replenishment and release at the photoreceptor synapse to better…
Many important multi-component crystalline solids undergo mechanochemical spinodal decomposition: a phase transformation in which the compositional redistribution is coupled with structural changes of the crystal, resulting in dynamically…
We introduce a rigorous method to microscopically compute the observables which characterize the thermodynamics and kinetics of rare macromolecular transitions for which it is possible to identify a priori a slow reaction coordinate. In…
Modern buildings encompass complex dynamics of multiple electrical, mechanical, and control systems. One of the biggest hurdles in applying conventional model-based optimization and control methods to building energy management is the huge…
The rate of a chemical reaction can often be determined by the properties of a rank-1 saddle and the associated transition state separating reactants and products. We have found evidence that such rates can be controlled and even enhanced…
A dynamical neural network consists of a set of interconnected neurons that interact over time continuously. It can exhibit computational properties in the sense that the dynamical system's evolution and/or limit points in the associated…
Reaction-Diffusion (RD) systems provide a computational framework that governs many pattern formation processes in nature. Current RD system design practices boil down to trial-and-error parameter search. We propose a differentiable…