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Conventional neural networks are universal function approximators, but because they are unaware of underlying symmetries or physical laws, they may need impractically many training data to approximate nonlinear dynamics. Recently introduced…
Network representations can help reveal the behavior of complex systems. Useful information can be derived from the network properties and invariants, such as components, clusters or cliques, as well as from their changes over time. The…
This paper focuses on the data-insufficiency problem in multi-task learning within an episodic training setup. Specifically, we explore the potential of heterogeneous information across tasks and meta-knowledge among episodes to effectively…
Simplicial map neural networks (SMNNs) are topology-based neural networks with interesting properties such as universal approximation ability and robustness to adversarial examples under appropriate conditions. However, SMNNs present some…
Irregularly-sampled time series occur in many domains including healthcare. They can be challenging to model because they do not naturally yield a fixed-dimensional representation as required by many standard machine learning models. In…
Translating non-invasive signals such as photoplethysmography (PPG) and ballistocardiography (BCG) into clinically meaningful signals like arterial blood pressure (ABP) is vital for continuous, low-cost healthcare monitoring. However,…
We provide a novel Neural Network architecture that can: i) output R-matrix for a given quantum integrable spin chain, ii) search for an integrable Hamiltonian and the corresponding R-matrix under assumptions of certain symmetries or other…
We study the problem of Hamiltonian structure learning from real-time evolution: given the ability to apply $e^{-\mathrm{i} Ht}$ for an unknown local Hamiltonian $H = \sum_{a = 1}^m \lambda_a E_a$ on $n$ qubits, the goal is to recover $H$.…
Time-series is ubiquitous across applications, such as transportation, finance and healthcare. Time-series is often influenced by external factors, especially in the form of asynchronous events, making forecasting difficult. However,…
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…
Pseudo-Hamiltonian neural networks (PHNN) were recently introduced for learning dynamical systems that can be modelled by ordinary differential equations. In this paper, we extend the method to partial differential equations. The resulting…
Modern IT system operation demands the integration of system software and hardware metrics. As a result, it generates a massive amount of data, which can be potentially used to make data-driven operational decisions. In the basic form, the…
We propose a time-multiplexed photonic network architecture based on coupled ring resonators, capable of accurately emulating specific Hamiltonian dynamics. We show that, in the Suzuki-Trotter limit, the resulting stroboscopic evolution…
Inductive bias refers to restrictions on the hypothesis class that enable a learning method to generalize effectively from limited data. A canonical example in control is linearity, which underpins low sample-complexity guarantees for…
Temporal Neural Networks (TNNs) are spiking neural networks that use time as a resource to represent and process information, similar to the mammalian neocortex. In contrast to compute-intensive deep neural networks that employ separate…
Simple Temporal Networks (STNs) provide a powerful and general tool for representing conjunctions of maximum delay constraints over ordered pairs of temporal variables. In this paper we introduce Hyper Temporal Networks (HyTNs), a strict…
Hybrid quantum systems with different particle species are fundamental in quantum materials and quantum information science. In this work, we establish a rigorous theoretical framework proving that, given access to an unknown spin-boson…
Accurate temporal extrapolation remains a fundamental challenge for neural operators modeling dynamical systems, where predictions must extend far beyond the training horizon. Conventional DeepONet approaches rely on two limited paradigms:…
Multiscale is a hallmark feature of complex nonlinear systems. While the simulation using the classical numerical methods is restricted by the local \textit{Taylor} series constraints, the multiscale techniques are often limited by finding…
We explore the construction of new symplectic numerical integration schemes to be used in Hamiltonian Monte Carlo and study their efficiency. Two integration schemes from Blanes et al. (2014), and a new scheme based on optimal acceptance…