Related papers: Dynamical large deviations of two-dimensional kine…
We use projected entangled-pair states (PEPS) to calculate the large deviations (LD) statistics of the dynamical activity of the two dimensional East model, and the two dimensional symmetric simple exclusion process (SSEP) with open…
A new approach for efficiently exploring the configuration space and computing the free energy of large atomic and molecular systems is proposed, motivated by an analogy with reinforcement learning. There are two major components in this…
We show that a neural network originally designed for language processing can learn the dynamical rules of a stochastic system by observation of a single dynamical trajectory of the system, and can accurately predict its emergent behavior…
Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…
Deep neural networks have been shown to provide accurate function approximations in high dimensions. However, fitting network parameters requires informative training data that are often challenging to collect in science and engineering…
Dynamic neural network is an emerging research topic in deep learning. Compared to static models which have fixed computational graphs and parameters at the inference stage, dynamic networks can adapt their structures or parameters to…
Classical methods of solving spatiotemporal dynamical systems include statistical approaches such as autoregressive integrated moving average, which assume linear and stationary relationships between systems' previous outputs. Development…
Neural population activity exhibits complex, nonlinear dynamics, varying in time, over trials, and across experimental conditions. Here, we develop Conditionally Linear Dynamical System (CLDS) models as a general-purpose method to…
A properly designed controller can help improve the quality of experimental measurements or force a dynamical system to follow a completely new time-evolution path. Recent developments in deep reinforcement learning have made steep advances…
Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…
Parameterized quantum circuits can be used as quantum neural networks and have the potential to outperform their classical counterparts when trained for addressing learning problems. To date, much of the results on their performance on…
Mean field theory has been successfully used to analyze deep neural networks (DNN) in the infinite size limit. Given the finite size of realistic DNN, we utilize the large deviation theory and path integral analysis to study the deviation…
The mean-field theory of Kinetically-Constrained-Models is developed by considering the Fredrickson-Andersen model on the Bethe lattice. Using certain properties of the dynamics observed in actual numerical experiments we derive asymptotic…
Deep neural networks (DNNs) achieve remarkable performance on a wide range of tasks, yet their mathematical analysis remains fragmented: stability and generalization are typically studied in disparate frameworks and on a case-by-case basis.…
We introduce a new class of non-linear models for functional data based on neural networks. Deep learning has been very successful in non-linear modeling, but there has been little work done in the functional data setting. We propose two…
Most existing neural network-based approaches for solving stochastic optimal control problems using the associated backward dynamic programming principle rely on the ability to simulate the underlying state variables. However, in some…
We study the non-equilibrium dynamics of the dissipative quantum East model via numerical tensor networks. We use matrix product states to represent evolution under quantum-jump unravellings for sizes beyond those accessible to exact…
Fine-tuning pretrained models has become a standard approach to adapting pretrained knowledge to improve the accuracy on new sparse, imbalance datasets. However, issues arise when optimization falls into a collapsed state, where the model…
We introduce a scalable variational method for simulating the dynamics of interacting open quantum bosonic systems deep in the quantum regime. The method is based on a multi-dimensional Wigner phase-space representation and employs a…
We study the asymptotics of a two-dimensional stochastic differential system with a degenerate diffusion matrix. This system describes the dynamics of a population where individuals contribute to the degradation of their environment through…