Related papers: Foundation Inference Models for Ordinary Different…

End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics.…

Traditional radio map estimation (RME) techniques fail to capture multi-dimensional and dynamic characteristics of complex spectrum environments. Recent data-driven methods achieve accurate RME in spatial domain, but ignore physical prior…

Parameter estimation for ordinary differential equations (ODEs) plays a fundamental role in the analysis of dynamical systems. Generally lacking closed-form solutions, ODEs are traditionally approximated using deterministic solvers.…

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…

Learning robust vision models that perform well in out-of-distribution (OOD) situations is an important task for model deployment in real-world settings. Despite extensive research in this field, many proposed methods have only shown minor…

Partial differential equations (PDEs) govern a wide range of physical systems, but solving them efficiently remains a major challenge. The idea of a scientific foundation model (SciFM) is emerging as a promising tool for learning…

The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…

Out-of-Distribution (OOD) detection is crucial when deploying machine learning models in open-world applications. The core challenge in OOD detection is mitigating the model's overconfidence on OOD data. While recent methods using auxiliary…

Diffusion Probabilistic Models (DPMs) have shown remarkable potential in image generation, but their sampling efficiency is hindered by the need for numerous denoising steps. Most existing solutions accelerate the sampling process by…

Streamlined qBOLD acquisitions enable experimentally straightforward observations of brain oxygen metabolism. $R_2^\prime$ maps are easily inferred; however, the Oxygen extraction fraction (OEF) and deoxygenated blood volume (DBV) are more…

Neural ordinary differential equations (NODE) have been proposed as a continuous depth generalization to popular deep learning models such as Residual networks (ResNets). They provide parameter efficiency and automate the model selection…

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…

Augmenting mechanistic ordinary differential equation (ODE) models with machine-learnable structures is an novel approach to create highly accurate, low-dimensional models of engineering systems incorporating both expert knowledge and…

Diffusion and Schr\"{o}dinger Bridge models have established state-of-the-art performance in generative modeling but are often hampered by significant computational costs and complex training procedures. While continuous-time bridges…

Stiff ordinary differential equations (ODEs) are common in many science and engineering fields, but standard neural ODE approaches struggle to accurately learn these stiff systems, posing a significant barrier to widespread adoption of…

It was recently shown that neural ordinary differential equation models cannot solve fundamental and seemingly straightforward tasks even with high-capacity vector field representations. This paper introduces two other fundamental tasks to…

We present a novel approach that redefines the traditional interpretation of explicit and implicit discretization methods for solving a general class of advection-diffusion equations (ADEs) featuring nonlinear advection, diffusion…

We investigate a novel approach to time-series modeling, inspired by the successes of large pretrained foundation models. We introduce FAE (Foundation Auto-Encoders), a foundation generative-AI model for anomaly detection in time-series…

Efficient and effective Out-of-Distribution (OOD) detection is essential for the safe deployment of AI systems. Existing feature space methods, while effective, often incur significant computational overhead due to their reliance on…

This paper presents a physics-informed training framework for projection-based Reduced Order Models (ROMs). We extend the PROM-ANN architecture by complementing snapshot-based training with a FEM-based, discrete physics-informed residual…