Chemical reaction networks (CRNs), defined by sets of species and possible reactions
between them, are widely used to interrogate chemical systems. To capture increasingly …

The conjoining of dynamical systems and deep learning has become a topic of great
interest. In particular, neural differential equations (NDEs) demonstrate that neural networks …

Denoising diffusion probabilistic models (DDPMs) have achieved high quality image
generation without adversarial training, yet they require simulating a Markov chain for many …

We propose a novel class of graph neural networks based on the discretized Beltrami flow, a
non-Euclidean diffusion PDE. In our model, node features are supplemented with positional …

Time series modeling is a well-established problem, which often requires that methods (1)
expressively represent complicated dependencies,(2) forecast long horizons, and (3) …

Neural ordinary differential equations (neural ODEs) are a popular family of continuous-
depth deep learning models. In this work, we consider a large family of parameterized ODEs …

The development of data-informed predictive models for dynamical systems is of
widespread interest in many disciplines. We present a unifying framework for blending …

The combination of ordinary differential equations and neural networks, ie, neural ordinary
differential equations (Neural ODE), has been widely studied from various angles. However …

The self-attention mechanism (SAM) is widely used in various fields of artificial intelligence
and has successfully boosted the performance of different models. However, current …

We provide a general framework for studying recurrent neural networks (RNNs) trained by
injecting noise into hidden states. Specifically, we consider RNNs that can be viewed as …