Related papers: Physiome-ODE: A Benchmark for Irregularly Sampled …
Partial differential equations (PDEs) govern a wide range of physical systems, and recent multimodal foundation models have shown promise for learning PDE solution operators across diverse equation families. However, existing multi-operator…
Estimating counterfactual outcomes over time has the potential to unlock personalized healthcare by assisting decision-makers to answer ''what-iF'' questions. Existing causal inference approaches typically consider regular, discrete-time…
We propose a machine learning framework to accelerate numerical computations of time-dependent ODEs and PDEs. Our method is based on recasting (generalizations of) existing numerical methods as artificial neural networks, with a set of…
Simple models have been used to describe ecological processes for over a century. However, the complexity of ecological systems makes simple models subject to modeling bias due to simplifying assumptions or unaccounted factors, limiting…
We propose a continuous neural network architecture, termed Explainable Tensorized Neural Ordinary Differential Equations (ETN-ODE), for multi-step time series prediction at arbitrary time points. Unlike the existing approaches, which…
Foundation models for partial differential equations (PDEs) have emerged as powerful surrogates pre-trained on diverse physical systems, but adapting them to new downstream tasks remains challenging due to limited task-specific data and…
Irregularly sampled multivariate time series (ISMTS) are prevalent in reality. Most existing methods treat ISMTS as synchronized regularly sampled time series with missing values, neglecting that the irregularities are primarily attributed…
Telemetry streams from large-scale Internet-connected systems (e.g., IoT deployments and online platforms) naturally form an irregular multivariate time series (IMTS) whose accurate forecasting is operationally vital. A closer examination…
Spurred by tremendous success in pattern matching and prediction tasks, researchers increasingly resort to machine learning to aid original scientific discovery. Given large amounts of observational data about a system, can we uncover the…
Time series models are ubiquitous in science, arising in any situation where researchers seek to understand how a system's behaviour changes over time. A key problem in time series modelling is \emph{inference}; determining properties of…
In this work we develop an ordinary differential equations (ODE) model of physiological regulation of glycemia in type 1 diabetes mellitus (T1DM) patients in response to meals and intravenous insulin infusion. Unlike for the majority of…
Recent research in non-intrusive data-driven model order reduction (MOR) enabled accurate and efficient approximation of parameterized ordinary differential equations (ODEs). However, previous studies have focused on constant parameters,…
In real-world scenarios like traffic and energy, massive time-series data with missing values and noises are widely observed, even sampled irregularly. While many imputation methods have been proposed, most of them work with a local…
Supervised learning with irregularly sampled time series have been a challenge to Machine Learning methods due to the obstacle of dealing with irregular time intervals. Some papers introduced recently recurrent neural network models that…
Under a smart grid paradigm, there has been an increase in sensor installations to enhance situational awareness. The measurements from these sensors can be leveraged for real-time monitoring, control, and protection. However, these…
Learning large scale nonlinear ordinary differential equation (ODE) systems from data is known to be computationally and statistically challenging. We present a framework together with the adaptive integral matching (AIM) algorithm for…
Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the…
Neural ODEs (NODEs) have emerged as powerful tools for modeling time series data, offering the flexibility to adapt to varying input scales and capture complex dynamics. However, they face significant challenges: first, their reliance on…
This review maps developments in stochastic modeling, highlighting non-standard approaches and their applications to biology and epidemiology. It brings together four strands: (1) core models for systems that evolve with randomness; (2)…
The understanding and modeling of complex physical phenomena through dynamical systems has historically driven scientific progress, as it provides the tools for predicting the behavior of different systems under diverse conditions through…