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This paper is concerned with the utilization of deterministically modeled chemical reaction networks for the implementation of (feed-forward) neural networks. We develop a general mathematical framework and prove that the ordinary…
A large body of work has suggested that neural populations exhibit low-dimensional dynamics during behavior. However, there are a variety of different approaches for modeling low-dimensional neural population activity. One approach involves…
The use of deep neural network (DNN) models as surrogates for linear and nonlinear structural dynamical systems is explored. The goal is to develop DNN based surrogates to predict structural response, i.e., displacements and accelerations,…
Event-based cameras are inspired by the sparse and asynchronous spike representation of the biological visual system. However, processing the event data requires either using expensive feature descriptors to transform spikes into frames, or…
We introduce a method for manipulating objects in three-dimensional space using controlled fluid streams. To achieve this, we train a neural network controller in a differentiable simulation and evaluate it in a simulated environment…
Data-driven inference of the generative dynamics underlying a set of observed time series is of growing interest in machine learning and the natural sciences. In neuroscience, such methods promise to alleviate the need to handcraft models…
A novel hybrid deep neural network architecture is designed to capture the spatial-temporal features of unsteady flows around moving boundaries directly from high-dimensional unsteady flow fields data. The hybrid deep neural network is…
Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…
This paper is concerned with classes of models of stochastic reaction dynamics with time-scales separation. We demonstrate that the existence of the time-scale separation naturally leads to the application of the averaging principle and…
The paper studies the problem of detecting and locating change points in multivariate time-evolving data. The problem has a long history in statistics and signal processing and various algorithms have been developed primarily for simple…
Chemical reaction networks are widely used to model stochastic dynamics in chemical kinetics, systems biology and epidemiology. Solving the chemical master equation that governs these systems poses a significant challenge due to the large…
In molecular dynamics (MD), neural network (NN) potentials trained bottom-up on quantum mechanical data have seen tremendous success recently. Top-down approaches that learn NN potentials directly from experimental data have received less…
We give the first provably efficient algorithms for learning neural networks with distribution shift. We work in the Testable Learning with Distribution Shift framework (TDS learning) of Klivans et al. (2024), where the learner receives…
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…
We develop a backward-in-time machine learning algorithm that uses a sequence of neural networks to solve optimal switching problems in energy production, where electricity and fossil fuel prices are subject to stochastic jumps. We then…
We introduce a dynamical spatio-temporal model formalized as a recurrent neural network for forecasting time series of spatial processes, i.e. series of observations sharing temporal and spatial dependencies. The model learns these…
Using random walk sampling methods for feature learning on networks, we develop a method for generating low-dimensional node embeddings for directed graphs and identifying transition states of stochastic chemical reacting systems. We…
We propose and demonstrate a nonlinear control method that can be applied to unknown, complex systems where the controller is based on a type of artificial neural network known as a reservoir computer. In contrast to many modern…
The dynamics of temporal networks lie in the continuous interactions between nodes, which exhibit the dynamic node preferences with time elapsing. The challenges of mining temporal networks are thus two-fold: the dynamic structure of…
We present a structured neural network architecture that is inspired by linear time-varying dynamical systems. The network is designed to mimic the properties of linear dynamical systems which makes analysis and control simple. The…