Related papers: Neural SDEs as a Unified Approach to Continuous-Do…
Latent neural stochastic differential equations (SDEs) have recently emerged as a promising approach for learning generative models from stochastic time series data. However, they systematically underestimate the noise level inherent in…
Dosing models often use differential equations to model biological dynamics. Neural differential equations in particular can learn to predict the derivative of a process, which permits predictions at irregular points of time. However, this…
Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…
Neural Ordinary Differential Equations (NODEs) use a neural network to model the instantaneous rate of change in the state of a system. However, despite their apparent suitability for dynamics-governed time-series, NODEs present a few…
Representations of sequential data are commonly based on the assumption that observed sequences are realizations of an unknown underlying stochastic process, where the learning problem includes determination of the model parameters. In this…
Many successful methods to learn dynamical systems from data have recently been introduced. However, ensuring that the inferred dynamics preserve known constraints, such as conservation laws or restrictions on the allowed system states,…
This article develops a stochastic differential equation (SDE) for modeling the temporal evolution of queue length dynamics at signalized intersections. Inspired by the observed quasiperiodic and self-similar characteristics of the queue…
The manifold hypothesis suggests that high-dimensional neural time series lie on a low-dimensional manifold shaped by simpler underlying dynamics. To uncover this structure, latent dynamical variable models such as state-space models,…
Neural Controlled Differential Equations (NCDEs) are a state-of-the-art tool for supervised learning with irregularly sampled time series (Kidger, 2020). However, no theoretical analysis of their performance has been provided yet, and it…
Scientific machine learning is an emerging field that broadly describes the combination of scientific computing and machine learning to address challenges in science and engineering. Within the context of differential equations, this has…
Non-uniform sampling arises when an experimenter does not have full control over the sampling characteristics of the process under investigation. Moreover, it is introduced intentionally in algorithms such as Bayesian optimization and…
Controlling continuous-time dynamical systems is generally a two step process: first, identify or model the system dynamics with differential equations, then, minimize the control objectives to achieve optimal control function and optimal…
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…
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 and differential equation are two sides of the same coin.…
While exogenous variables have a major impact on performance improvement in time series analysis, inter-series correlation and time dependence among them are rarely considered in the present continuous methods. The dynamical systems of…
Generating high-quality time series data has emerged as a critical research topic due to its broad utility in supporting downstream time series mining tasks. A major challenge lies in modeling the intrinsic stochasticity of temporal…
Modeling stochastic and irregularly sampled time series is a challenging problem found in a wide range of applications, especially in medicine. Neural stochastic differential equations (Neural SDEs) are an attractive modeling technique for…
We present a novel deep learning method for estimating time-dependent parameters in Markov processes through discrete sampling. Departing from conventional machine learning, our approach reframes parameter approximation as an optimization…
Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…
We develop a new continuous-time stochastic gradient descent method for optimizing over the stationary distribution of stochastic differential equation (SDE) models. The algorithm continuously updates the SDE model's parameters using an…