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The time evolution of dynamical systems is frequently described by ordinary differential equations (ODEs), which must be solved for given initial conditions. Most standard approaches numerically integrate ODEs producing a single solution…

To derive the hidden dynamics from observed data is one of the fundamental but also challenging problems in many different fields. In this study, we propose a new type of interpretable network called the ordinary differential equation…

Neural ordinary differential equations (Neural ODEs) are an effective framework for learning dynamical systems from irregularly sampled time series data. These models provide a continuous-time latent representation of the underlying…

In real-world systems, phase transitions often materialize abruptly, making it difficult to design appropriate controls that help uncover underlying processes. Some agent-based computational models display transformations similar to phase…

Methods based on ordinary differential equations (ODEs) are widely used to build generative models of time-series. In addition to high computational overhead due to explicitly computing hidden states recurrence, existing ODE-based models…

We propose a new method to ensure neural ordinary differential equations (ODEs) satisfy output specifications by using invariance set propagation. Our approach uses a class of control barrier functions to transform output specifications…

Modeling neural population dynamics is crucial for foundational neuroscientific research and various clinical applications. Conventional latent variable methods typically model continuous brain dynamics through discretizing time with…

In most biological studies and processes, cell proliferation and population dynamics play an essential role. Due to this ubiquity, a multitude of mathematical models has been developed to describe these processes. While the simplest models…

Ordinary differential equations (ODEs) are the primary means to modelling dynamical systems in many natural and engineering sciences. The number of equations required to describe a system with high heterogeneity limits our capability of…

We develop a transformer-based sequence-to-sequence model that recovers scalar ordinary differential equations (ODEs) in symbolic form from irregularly sampled and noisy observations of a single solution trajectory. We demonstrate in…

Computational modeling of single-cell gene expression is crucial for understanding cellular processes, but generating realistic expression profiles remains a major challenge. This difficulty arises from the count nature of gene expression…

Deep generative models open new avenues for simulating realistic genomic data while preserving privacy and addressing data accessibility constraints. While previous studies have primarily focused on generating gene expression or haplotype…

Ordinary differential equations (ODEs) can model the transition of cell states over time. Bifurcation theory is a branch of dynamical systems which studies changes in the behavior of an ODE system while one or more parameters are varied. We…

Generative modeling and clustering are conventionally distinct tasks in machine learning. Variational Autoencoders (VAEs) have been widely explored for their ability to integrate both, providing a framework for generative clustering.…

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…

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…

Modern high-throughput biological datasets with thousands of perturbations provide the opportunity for large-scale discovery of causal graphs that represent the regulatory interactions between genes. Differentiable causal graphical models…

In this paper, we implement Neural Ordinary Differential Equations in a Variational Autoencoder setting for generative time series modeling. An object-oriented approach to the code was taken to allow for easier development and research and…

Recent methods have been developed to map single-cell lineage statistics to population growth. Because population growth selects for exponentially rare phenotypes, these methods inherently depend on sampling large deviations from finite…

Latent variable models such as the Variational Auto-Encoder (VAE) have become a go-to tool for analyzing biological data, especially in the field of single-cell genomics. One remaining challenge is the interpretability of latent variables…