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Neural ordinary differential equations (NODEs) treat computation of intermediate feature vectors as trajectories of ordinary differential equation parameterized by a neural network. In this paper, we propose a novel model, delay…

It has been observed that residual networks can be viewed as the explicit Euler discretization of an Ordinary Differential Equation (ODE). This observation motivated the introduction of so-called Neural ODEs, which allow more general…

Test time adaptation (TTA) has emerged as a promising solution to adapt pre-trained models to new, unseen data distributions using unlabeled target domain data. However, most TTA methods are designed for independent data, often overlooking…

The advancement of human healthspan and bioengineering relies heavily on predicting the behavior of complex biological systems. While high-throughput multiomics data is becoming increasingly abundant, converting this data into actionable…

We use neural ordinary differential equations to formulate a variant of the Transformer that is depth-adaptive in the sense that an input-dependent number of time steps is taken by the ordinary differential equation solver. Our goal in…

Session-based recommendation (SBR) aims to predict the user next action based on the ongoing sessions. Recently, there has been an increasing interest in modeling the user preference evolution to capture the fine-grained user interests.…

Neural Ordinary Differential Equations (Neural ODEs) represent continuous-time dynamics with neural networks, offering advancements for modeling and control tasks. However, training Neural ODEs requires solving differential equations at…

Neural ODE Processes approach the problem of meta-learning for dynamics using a latent variable model, which permits a flexible aggregation of contextual information. This flexibility is inherited from the Neural Process framework and…

Modeling real-world multidimensional time series can be particularly challenging when these are sporadically observed (i.e., sampling is irregular both in time and across dimensions)-such as in the case of clinical patient data. To address…

We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a…

We introduce Active Tuning, a novel paradigm for optimizing the internal dynamics of recurrent neural networks (RNNs) on the fly. In contrast to the conventional sequence-to-sequence mapping scheme, Active Tuning decouples the RNN's…

Neural Radiance Fields (NeRF)-based models have achieved remarkable success in 3D reconstruction and rendering tasks. However, during both training and inference, these models rely heavily on dense point sampling along rays from multiple…

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…

Random ordinary differential equations (RODEs), i.e. ODEs with random parameters, are often used to model complex dynamics. Most existing methods to identify unknown governing RODEs from observed data often rely on strong prior knowledge.…

Dissipative partial differential equations that exhibit chaotic dynamics tend to evolve to attractors that exist on finite-dimensional manifolds. We present a data-driven reduced order modeling method that capitalizes on this fact by…

Neural ordinary differential equations (NODEs) have been proven useful for learning non-linear dynamics of arbitrary trajectories. However, current NODE methods capture variations across trajectories only via the initial state value or by…

Ordinary differential equations (ODEs) can provide mechanistic models of temporally local changes of processes, where parameters are often informed by external knowledge. While ODEs are popular in systems modeling, they are less established…

We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations. In particular, given a time-series or spatio-temporal dataset, we seek to identify an accurate governing…

Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. Here, we explore the use of Neural Ordinary Differential Equations, a recently introduced family of…