Related papers: Deep Hamiltonian networks based on symplectic inte…

Machine learning frameworks for physical problems must capture and enforce physical constraints that preserve the structure of dynamical systems. Many existing approaches achieve this by integrating physical operators into neural networks.…

The fundamental laws of physics are intrinsically geometric, dictating the evolution of systems through principles of symmetry and conservation. While modern machine learning offers powerful tools for modeling complex dynamics from data,…

Deep neural networks are powerful tools for solving nonlinear problems in science and engineering, but training highly accurate models becomes challenging as problem complexity increases. Non-convex optimization and sensitivity to…

The paper intends to lay out the first steps towards constructing a unified framework to understand the symplectic and spectral theory of finite dimensional integrable Hamiltonian systems. While it is difficult to know what the best…

An important difference between brains and deep neural networks is the way they learn. Nervous systems learn online where a stream of noisy data points are presented in a non-independent, identically distributed (non-i.i.d.) way. Further,…

This paper establishes statistical properties of deep neural network (DNN) estimators under dependent data. Two general results for nonparametric sieve estimators directly applicable to DNN estimators are given. The first establishes rates…

Even though Deep Neural Networks (DNNs) are widely celebrated for their practical performance, they possess many intriguing properties related to depth that are difficult to explain both theoretically and intuitively. Understanding how…

In the context of classification problems, Deep Learning (DL) approaches represent state of art. Many DL approaches are based on variations of standard multi-layer feed-forward neural networks. These are also referred to as deep networks.…

This paper presents a method for learning Hamiltonian dynamics from a limited set of data points. The Hamiltonian vector field is found by regularized optimization over a reproducing kernel Hilbert space of vector fields that are inherently…

Many learning problems involve symmetries, and while invariance can be built into neural architectures, it can also emerge implicitly when training on group-structured data. We study this phenomenon in classical Hopfield networks and show…

This article considers Hamiltonian mechanical systems with potential functions admitting jump discontinuities. The focus is on accurate and efficient numerical approximations of their solutions, which will be defined via the laws of…

As neural networks grow deeper and wider, learning networks with hard-threshold activations is becoming increasingly important, both for network quantization, which can drastically reduce time and energy requirements, and for creating large…

In this paper we propose a novel neural network model for learning stochastic Hamiltonian systems (SHSs) from observational data, termed the stochastic generating function neural network (SGFNN). SGFNN preserves symplectic structure of the…

In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…

Deep hedging uses recurrent neural networks to hedge financial products that cannot be fully hedged in incomplete markets. Previous work in this area focuses on minimizing some measure of quadratic hedging error by calculating pathwise…

In this study, we focus on learning Hamiltonian systems, which involves predicting the coordinate (q) and momentum (p) variables generated by a symplectic mapping. Based on Chen & Tao (2021), the symplectic mapping is represented by a…

Hamiltonian neural networks (HNNs) represent a promising class of physics-informed deep learning methods that utilize Hamiltonian theory as foundational knowledge within neural networks. However, their direct application to engineering…

Heterogeneous graph neural networks (HGNNs) have attracted increasing research interest in recent three years. Most existing HGNNs fall into two classes. One class is meta-path-based HGNNs which either require domain knowledge to handcraft…

Learning workable representations of dynamical systems is becoming an increasingly important problem in a number of application areas. By leveraging recent work connecting deep neural networks to systems of differential equations, we…

In this paper, we present a novel hybrid deep learning model, named ConvLSTMTransNet, designed for time series prediction, with a specific application to internet traffic telemetry. This model integrates the strengths of Convolutional…