Related papers: A convolutional autoencoder and neural ODE framewo…
We propose Characteristic-Neural Ordinary Differential Equations (C-NODEs), a framework for extending Neural Ordinary Differential Equations (NODEs) beyond ODEs. While NODEs model the evolution of a latent variables as the solution to an…
Inverse modeling for the estimation of non-Gaussian hydraulic conductivity fields in subsurface flow and solute transport models remains a challenging problem. This is mainly due to the non-Gaussian property, the non-linear physics, and the…
Diffractive deep neural network (D2NN), known for its high speed and strong parallelism, has been widely applied across various fields, including pattern recognition, image processing, and image transmission. However, existing network…
Simultaneous recordings from thousands of neurons across multiple brain areas reveal rich mixtures of activity that are shared between regions and dynamics that are unique to each region. Existing alignment or multi-view methods neglect…
Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.…
Surrogate strategies are used widely for uncertainty quantification of groundwater models in order to improve computational efficiency. However, their application to dynamic multiphase flow problems is hindered by the curse of…
Variational Autoencoders (VAEs) are a powerful framework for learning latent representations of reduced dimensionality, while Neural ODEs excel in learning transient system dynamics. This work combines the strengths of both to generate fast…
Many physical systems exhibit a low-dimensional structure that varies with external parameters: link lengths in a robot, forcing constants in a fluid, or Reynolds numbers in a flow shift the underlying manifold while preserving its…
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…
A combined convolutional autoencoder-recurrent neural network machine learning model is presented to analyse and forecast the dynamics and low-order statistics of the local convective heat flux field in a two-dimensional turbulent…
While tumor dynamic modeling has been widely applied to support the development of oncology drugs, there remains a need to increase predictivity, enable personalized therapy, and improve decision-making. We propose the use of Tumor Dynamic…
We propose a deep probabilistic-neural-network architecture for learning a minimal and near-orthogonal set of non-linear modes from high-fidelity turbulent-flow-field data useful for flow analysis, reduced-order modeling, and flow control.…
We propose a non-intrusive, Autoencoder-based framework for reduced-order modeling in continuum mechanics. Our method integrates three stages: (i) an unsupervised Autoencoder compresses high-dimensional finite element solutions into a…
In this paper, an end-to-end nonlinear model reduction methodology is presented based on the convolutional recurrent autoencoder networks. The methodology is developed in the context of the overall data-driven reduced-order model framework…
We propose a customized convolutional neural network based autoencoder called a hierarchical autoencoder, which allows us to extract nonlinear autoencoder modes of flow fields while preserving the contribution order of the latent vectors.…
The use of deep learning has become increasingly popular in reduced-order models (ROMs) to obtain low-dimensional representations of full-order models. Convolutional autoencoders (CAEs) are often used to this end as they are adept at…
Counterfactual explanations (CEs) aim to enhance the interpretability of machine learning models by illustrating how alterations in input features would affect the resulting predictions. Common CE approaches require an additional model and…
Learning-based surrogate models have become a practical alternative to high-fidelity CFD solvers, but their latent representations remain opaque and hinder adoption in safety-critical or regulation-bound settings. This work introduces a…
We designed a new artificial neural network by modifying the neural ordinary differential equation (NODE) framework to successfully predict the time evolution of the 2D mode profile in both the linear growth and nonlinear saturated stages.…
A combined autoencoder (AE) and neural ordinary differential equation (NODE) framework has been used as a data-driven reduced-order model for time integration of a stiff reacting system. In this study, a new loss term using a latent…