# Model Reduction and Neural Networks

**Type:** Topics  
**Canonical URL:** https://scholariq.org/topics/model-reduction-and-neural-networks/

## Facts

| Field | Value |
| --- | --- |
| Description | This cluster of papers focuses on the development and application of physics-informed neural networks for scientific computing, particularly in the context of solving partial differential equations, model reduction, fluid dynamics, dynamic mode decomposition, and nonlinear systems. The research explores the integration of deep learning techniques with traditional numerical methods to address complex problems in physics-based modeling and simulation. |
| Domain | Physical Sciences |
| Field | Physics and Astronomy |
| OpenAlex ID | t11206 |
| Works | 27 |

## Topic papers all

Showing 15 of 27.

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://scholariq.org/papers/score-based-generative-modeling-through-stochastic-differential-equations/)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://scholariq.org/papers/fourier-neural-operator-for-parametric-partial-differential-equations/)
- [Physics-informed machine learning: case studies for weather and climate modelling](https://scholariq.org/papers/physics-informed-machine-learning-case-studies-for-weather-and-climate-modelling/)
- [Integrating machine learning and multiscale modeling—perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences](https://scholariq.org/papers/integrating-machine-learning-and-multiscale-modeling-perspectives-challenges-and/)
- [U-FNO—An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://scholariq.org/papers/u-fno-an-enhanced-fourier-neural-operator-based-deep-learning-model-for/)
- [Multiscale modeling meets machine learning: What can we learn?](https://scholariq.org/papers/multiscale-modeling-meets-machine-learning-what-can-we-learn/)
- [A new active labeling method for deep learning](https://scholariq.org/papers/a-new-active-labeling-method-for-deep-learning/)
- [Neural operators for accelerating scientific simulations and design](https://scholariq.org/papers/neural-operators-for-accelerating-scientific-simulations-and-design/)
- [Neural-Fly enables rapid learning for agile flight in strong winds](https://scholariq.org/papers/neural-fly-enables-rapid-learning-for-agile-flight-in-strong-winds/)
- [SIMULATING THE FLUID DYNAMICS OF NATURAL AND PROSTHETIC HEART VALVES USING THE IMMERSED BOUNDARY METHOD](https://scholariq.org/papers/simulating-the-fluid-dynamics-of-natural-and-prosthetic-heart-valves-using-the/)
- [Space–time fractional Schrödinger equation with time-independent potentials](https://scholariq.org/papers/space-time-fractional-schrodinger-equation-with-time-independent-potentials/)
- [Solution of physics-based Bayesian inverse problems with deep generative priors](https://scholariq.org/papers/solution-of-physics-based-bayesian-inverse-problems-with-deep-generative-priors/)
- [Assessing the stability of linear time-invariant continuous interval dynamic systems](https://scholariq.org/papers/assessing-the-stability-of-linear-time-invariant-continuous-interval-dynamic/)
- [Fast explicit dynamics finite element algorithm for transient heat transfer](https://scholariq.org/papers/fast-explicit-dynamics-finite-element-algorithm-for-transient-heat-transfer/)
- [Numerical solving of the generalized Black-Scholes differential equation using Laguerre neural network](https://scholariq.org/papers/numerical-solving-of-the-generalized-black-scholes-differential-equation-using/)

## Topic primary papers

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://scholariq.org/papers/fourier-neural-operator-for-parametric-partial-differential-equations/)
- [Integrating machine learning and multiscale modeling—perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences](https://scholariq.org/papers/integrating-machine-learning-and-multiscale-modeling-perspectives-challenges-and/)
- [U-FNO—An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://scholariq.org/papers/u-fno-an-enhanced-fourier-neural-operator-based-deep-learning-model-for/)
- [Neural operators for accelerating scientific simulations and design](https://scholariq.org/papers/neural-operators-for-accelerating-scientific-simulations-and-design/)
- [Group-wise construction of reduced models for understanding and characterization of pulmonary blood flows from medical images](https://scholariq.org/papers/group-wise-construction-of-reduced-models-for-understanding-and-characterization/)
- [SNODE: Spectral Discretization of Neural ODEs for System Identification](https://scholariq.org/papers/snode-spectral-discretization-of-neural-odes-for-system-identification/)
- [Variationally mimetic operator networks](https://scholariq.org/papers/variationally-mimetic-operator-networks/)
- [Scalable Transformer for PDE Surrogate Modeling](https://scholariq.org/papers/scalable-transformer-for-pde-surrogate-modeling/)
- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://scholariq.org/papers/a-physics-informed-diffusion-model-for-high-fidelity-flow-field-reconstruction/)

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Source: ScholarIQ — public research metadata, principally OpenAlex. See https://scholariq.org/sources/ for provenance and https://scholariq.org/methodology/ for what these figures mean.