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Classic algorithms and machine learning systems like neural networks are both abundant in everyday life. While classic computer science algorithms are suitable for precise execution of exactly defined tasks such as finding the shortest path…

Machine Learning · Computer Science 2022-09-02 Felix Petersen

Significant variations of delays among connecting neurons cause an inevitable disadvantage of asynchronous brain dynamics compared to synchronous deep learning. However, this study demonstrates that this disadvantage can be converted into a…

Biological Physics · Physics 2024-10-16 Yuval Meir , Ofek Tevet , Yarden Tzach , Shiri Hodassman , Ido Kanter

This work proposes an autoencoder neural network as a non-linear generalization of projection-based methods for solving Partial Differential Equations (PDEs). The proposed deep learning architecture presented is capable of generating the…

Computational Physics · Physics 2020-06-25 Jaime Lopez Garcia , Angel Rivero Jimenez

Deep sequence models have achieved notable success in time-series analysis, such as interpolation and forecasting. Recent advances move beyond discrete-time architectures like Recurrent Neural Networks (RNNs) toward continuous-time…

Machine Learning · Computer Science 2025-08-05 Haoran Li , Muhao Guo , Yang Weng , Hanghang Tong

Augmenting mechanistic ordinary differential equation (ODE) models with machine-learnable structures is an novel approach to create highly accurate, low-dimensional models of engineering systems incorporating both expert knowledge and…

Dynamical Systems · Mathematics 2022-06-22 Sandor Beregi , David A. W. Barton , Djamel Rezgui , Simon A. Neild

We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…

Statistical Mechanics · Physics 2011-10-11 P. L. Krapivsky , J. M. Luck , K. Mallick

The information of spiking neural networks (SNNs) are propagated between the adjacent biological neuron by spikes, which provides a computing paradigm with the promise of simulating the human brain. Recent studies have found that the time…

Neural and Evolutionary Computing · Computer Science 2022-05-05 Pengfei Sun , Longwei Zhu , Dick Botteldooren

Systems whose time evolutions are entirely deterministic can nevertheless be studied probabilistically, i.e. in terms of the evolution of probability distributions rather than individual trajectories. This approach is central to the…

Dynamical Systems · Mathematics 2019-09-06 S. Richard Taylor

The advancement of human healthspan and bioengineering relies heavily on predicting the behavior of complex biological systems. While high-throughput multiomics data is becoming increasingly abundant, converting this data into actionable…

Machine Learning · Computer Science 2025-12-10 Udesh Habaraduwa , Andrei Lixandru

We develop a methodology to learn finitely generated random iterated function systems from time-series of partial observations using delay embeddings. We obtain a minimal model representation for the observed dynamics, using a hidden…

Dynamical Systems · Mathematics 2025-08-20 Emilia Gibson , Jeroen S. W. Lamb

Sequential-in-time methods solve a sequence of training problems to fit nonlinear parametrizations such as neural networks to approximate solution trajectories of partial differential equations over time. This work shows that…

Numerical Analysis · Mathematics 2024-04-02 Huan Zhang , Yifan Chen , Eric Vanden-Eijnden , Benjamin Peherstorfer

Neural controlled differential equations (CDEs) are the continuous-time analogue of recurrent neural networks, as Neural ODEs are to residual networks, and offer a memory-efficient continuous-time way to model functions of potentially…

Machine Learning · Computer Science 2021-06-22 James Morrill , Cristopher Salvi , Patrick Kidger , James Foster , Terry Lyons

By interpreting the forward dynamics of the latent representation of neural networks as an ordinary differential equation, Neural Ordinary Differential Equation (Neural ODE) emerged as an effective framework for modeling a system dynamics…

Machine Learning · Computer Science 2020-10-19 Daehoon Gwak , Gyuhyeon Sim , Michael Poli , Stefano Massaroli , Jaegul Choo , Edward Choi

In this paper we present a deep learning method to predict the temporal evolution of dissipative dynamic systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting…

Machine Learning · Computer Science 2022-06-07 Quercus Hernández , Alberto Badías , Francisco Chinesta , Elías Cueto

A problem related to the development of an algorithm designed to find an architecture of artificial neural network used for black-box modelling of dynamic systems with time delays has been addressed in this paper. The proposed algorithm is…

Neural and Evolutionary Computing · Computer Science 2023-11-03 Krzysztof Laddach , Rafał Łangowski

We analyze Neural Ordinary Differential Equations (NODEs) from a control theoretical perspective to address some of the main properties and paradigms of Deep Learning (DL), in particular, data classification and universal approximation.…

Optimization and Control · Mathematics 2021-04-13 Domènec Ruiz-Balet , Enrique Zuazua

A concept of using Neural Ordinary Differential Equations(NODE) for Transfer Learning has been introduced. In this paper we use the EfficientNets to explore transfer learning on CIFAR-10 dataset. We use NODE for fine-tuning our model. Using…

Machine Learning · Computer Science 2020-01-22 Rajath S , Sumukh Aithal K , Natarajan Subramanyam

Classical numerical methods for solving partial differential equations suffer from the curse dimensionality mainly due to their reliance on meticulously generated spatio-temporal grids. Inspired by modern deep learning based techniques for…

Machine Learning · Statistics 2018-04-20 Maziar Raissi

In this paper, we propose to model the video dynamics by learning the trajectory of independently inverted latent codes from GANs. The entire sequence is seen as discrete-time observations of a continuous trajectory of the initial latent…

Computer Vision and Pattern Recognition · Computer Science 2023-04-25 Weihao Xia , Yujiu Yang , Jing-Hao Xue

Differential equations are used to model problems that originate in disciplines such as physics, biology, chemistry, and engineering. In recent times, due to the abundance of data, there is an active search for data-driven methods to learn…

Machine Learning · Computer Science 2022-05-24 K. D. Olumoyin