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The recently-introduced class of ordinary differential equation networks (ODE-Nets) establishes a fruitful connection between deep learning and dynamical systems. In this work, we reconsider formulations of the weights as…

Developing tools for estimating heterogeneous treatment effects (HTE) and individualized treatment effects has been an area of active research in recent years. While these tools have proven to be useful in many contexts, a concern when…

Causal inference has gained much popularity in recent years, with interests ranging from academic, to industrial, to educational, and all in between. Concurrently, the study and usage of neural networks has also grown profoundly (albeit at…

This paper provides a solution to the evaluation of treatment effects in selective samples when neither instruments nor parametric assumptions are available. We provide sharp bounds for average treatment effects under a conditional…

Ordinary differential equations (ODEs) describe dynamical systems evolving deterministically in continuous time. Accurate data-driven modeling of systems as ODEs, a central problem across the natural sciences, remains challenging,…

Recent advancements in large language models (LLMs) based on transformer architectures have sparked significant interest in understanding their inner workings. In this paper, we introduce a novel approach to modeling transformer…

We propose a unified framework for delay differential equations (DDEs) based on deep neural networks (DNNs) - the neural delay differential equations (NDDEs), aimed at solving the forward and inverse problems of delay differential…

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…

There are many methods for finding a particular solution to a nonhomogeneous linear ordinary differential equation (ODE) with constant coefficients. The method of undetermined coefficients, Laplace transform method and differential operator…

Nonlinear operators with long distance spatiotemporal dependencies are fundamental in modeling complex systems across sciences, yet learning these nonlocal operators remains challenging in machine learning. Integral equations (IEs), which…

The neural Ordinary Differential Equation (ODE) model has shown success in learning complex continuous-time processes from observations on discrete time stamps. In this work, we consider the modeling and forecasting of time series data that…

Causal inference is essential for data-driven decision making across domains such as business engagement, medical treatment and policy making. However, research on causal discovery has evolved separately from inference methods, preventing…

Observational studies have recently received significant attention from the machine learning community due to the increasingly available non-experimental observational data and the limitations of the experimental studies, such as…

Neural Ordinary Differential Equations (NODEs) have proven to be a powerful modeling tool for approximating (interpolation) and forecasting (extrapolation) irregularly sampled time series data. However, their performance degrades…

As machine learning becomes increasingly prevalent in impactful decisions, recognizing when inference data is outside the model's expected input distribution is paramount for giving context to predictions. Out-of-distribution (OOD)…

Neural Ordinary Differential Equations (Neural ODEs) are the continuous analog of Residual Neural Networks (ResNets). We investigate whether the discrete dynamics defined by a ResNet are close to the continuous one of a Neural ODE. We first…

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…

To better understand and improve the behavior of neural networks, a recent line of works bridged the connection between ordinary differential equations (ODEs) and deep neural networks (DNNs). The connections are made in two folds: (1) View…

We study the problem of inferring heterogeneous treatment effects from time-to-event data. While both the related problems of (i) estimating treatment effects for binary or continuous outcomes and (ii) predicting survival outcomes have been…

Estimation of heterogeneous long-term treatment effects (HLTEs) is widely used for personalized decision-making in marketing, economics, and medicine, where short-term randomized experiments are often combined with long-term observational…