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Variational Autoencoders (VAEs) are a powerful framework for learning latent representations of reduced dimensionality, while Neural ODEs excel in learning transient system dynamics. This work combines the strengths of both to generate fast…
Variational Autoencoders (VAEs) are well-established as a principled approach to probabilistic unsupervised learning with neural networks. Typically, an encoder network defines the parameters of a Gaussian distributed latent space from…
Stochastic partial differential equations (SPDEs) describe the evolution of random processes over space and time, but their solutions are often analytically intractable and computationally expensive to estimate. In this paper, we propose…
Astronomical time series from large-scale surveys like LSST are often irregularly sampled and incomplete, posing challenges for classification and anomaly detection. We introduce a new framework based on Neural Stochastic Delay Differential…
We present a deep-learning Variational Encoder-Decoder (VED) framework for learning data-driven low-dimensional representations of the relationship between high-dimensional parameters of a physical system and the system's high-dimensional…
Clinical time series data from electronic health records and medical registries offer unprecedented opportunities to understand patient trajectories and inform medical decision-making. However, leveraging such data presents significant…
Neuromorphic hardware equipped with learning capabilities can adapt to new, real-time data. While models of Spiking Neural Networks (SNNs) can now be trained using gradient descent to reach an accuracy comparable to equivalent conventional…
Detecting anomalous edges and nodes in dynamic networks is critical in various areas, such as social media, computer networks, and so on. Recent approaches leverage network embedding technique to learn how to generate node representations…
Stochastic differential equations (SDEs) are a staple of mathematical modelling of temporal dynamics. However, a fundamental limitation has been that such models have typically been relatively inflexible, which recent work introducing…
In data-driven modeling of spatiotemporal phenomena careful consideration often needs to be made in capturing the dynamics of the high wavenumbers. This problem becomes especially challenging when the system of interest exhibits shocks or…
Stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) are fundamental for modeling stochastic dynamics across the natural sciences and modern machine learning. Learning their solution operators with…
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…
We propose a new class of physics-informed neural networks, called physics-informed Variational Autoencoder (PI-VAE), to solve stochastic differential equations (SDEs) or inverse problems involving SDEs. In these problems the governing…
AI models have garnered significant research attention towards predictive task automation. However, a stationary training environment is an underlying assumption for most models and such models simply do not work on non-stationary data…
Neural differential equation models have garnered significant attention in recent years for their effectiveness in machine learning applications.Among these, fractional differential equations (FDEs) have emerged as a promising tool due to…
Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great…
Neural Stochastic Differential Equations (Neural SDEs) provide a principled framework for modeling continuous-time stochastic processes and have been widely adopted in fields ranging from physics to finance. Recent advances suggest that…
We present a novel variational framework for performing inference in (neural) stochastic differential equations (SDEs) driven by Markov-approximate fractional Brownian motion (fBM). SDEs offer a versatile tool for modeling real-world…
A data-driven framework is proposed towards the end of predictive modeling of complex spatio-temporal dynamics, leveraging nested non-linear manifolds. Three levels of neural networks are used, with the goal of predicting the future state…
In deep latent Gaussian models, the latent variable is generated by a time-inhomogeneous Markov chain, where at each time step we pass the current state through a parametric nonlinear map, such as a feedforward neural net, and add a small…