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This paper integrates deep neural networks (DNNs) into structural economic models to increase flexibility and capture rich heterogeneity while preserving interpretability. Economic structure and machine learning are complements in empirical…

Econometrics · Economics 2025-04-28 Max H. Farrell , Tengyuan Liang , Sanjog Misra

The rise of Physics-Informed Neural Networks (PINNs) has popularized the concept of solving differential equations via residual minimization. However, neural networks are often viewed as ``black boxes" requiring significant computational…

Numerical Analysis · Mathematics 2026-05-20 Ayman Mourad , Fatima Mroue

We propose Gradient Informed Neural Networks (GradINNs), a methodology inspired by Physics Informed Neural Networks (PINNs) that can be used to efficiently approximate a wide range of physical systems for which the underlying governing…

Machine Learning · Computer Science 2024-09-04 Filippo Aglietti , Francesco Della Santa , Andrea Piano , Virginia Aglietti

Numerical modeling errors are unavoidable in finite element analysis. The presence of model errors inherently reflects both model accuracy and uncertainty. To date there have been few methods for explicitly quantifying errors at points of…

Machine Learning · Computer Science 2024-11-19 Bozhou Zhuang , Sashank Rana , Brandon Jones , Danny Smyl

We introduce the concept of a Graph-Informed Neural Network (GINN), a hybrid approach combining deep learning with probabilistic graphical models (PGMs) that acts as a surrogate for physics-based representations of multiscale and…

Computational Physics · Physics 2021-03-17 Eric J. Hall , Søren Taverniers , Markos A. Katsoulakis , Daniel M. Tartakovsky

Differential equations are indispensable to engineering and hence to innovation. In recent years, physics-informed neural networks (PINN) have emerged as a novel method for solving differential equations. PINN method has the advantage of…

Computational Engineering, Finance, and Science · Computer Science 2022-01-07 Mayank Raj , Pramod Kumbhar , Ratna Kumar Annabattula

We introduce a class of Sparse, Physics-based, and partially Interpretable Neural Networks (SPINN) for solving ordinary and partial differential equations (PDEs). By reinterpreting a traditional meshless representation of solutions of PDEs…

Machine Learning · Computer Science 2021-08-13 Amuthan A. Ramabathiran , Prabhu Ramachandran

Classical deep neural networks can learn rich multi-particle correlations in collider data, but their inductive biases are rarely anchored in physics structure. We propose quantum-informed neural networks (QINNs), a general framework that…

High Energy Physics - Phenomenology · Physics 2025-10-22 Aritra Bal , Markus Klute , Benedikt Maier , Melik Oughton , Eric Pezone , Michael Spannowsky

In this paper, we introduce a novel approach to neural learning: the Feature-Imitating-Network (FIN). A FIN is a neural network with weights that are initialized to reliably approximate one or more closed-form statistical features, such as…

Machine Learning · Computer Science 2021-10-26 Sari Saba-Sadiya , Tuka Alhanai , Mohammad M Ghassemi

We introduce a machine-learning framework named statistics-informed neural network (SINN) for learning stochastic dynamics from data. This new architecture was theoretically inspired by a universal approximation theorem for stochastic…

Machine Learning · Computer Science 2022-12-28 Yuanran Zhu , Yu-Hang Tang , Changho Kim

Physics-informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have…

Computational Engineering, Finance, and Science · Computer Science 2023-11-14 Ali Harandi , Ahmad Moeineddin , Michael Kaliske , Stefanie Reese , Shahed Rezaei

This paper proposes a novel neural network framework, denoted as spectral integrated neural networks (SINNs), for resolving three-dimensional forward and inverse dynamic problems. In the SINNs, the spectral integration method is applied to…

Numerical Analysis · Mathematics 2024-01-09 Lin Qiu , Fajie Wang , Wenzhen Qu , Yan Gu , Qing-Hua Qin

Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional…

Recently, physics-informed neural networks (PINNs) have offered a powerful new paradigm for solving problems relating to differential equations. Compared to classical numerical methods PINNs have several advantages, for example their…

Computational Physics · Physics 2024-06-21 Ben Moseley , Andrew Markham , Tarje Nissen-Meyer

Scientific modeling faces a tradeoff between the interpretability of mechanistic theory and the predictive power of machine learning. While existing hybrid approaches have made progress by incorporating domain knowledge into machine…

Machine Learning · Computer Science 2026-04-15 Carson Dudley , Reiden Magdaleno , Christopher Harding , Marisa Eisenberg

Physics-Informed Neural Networks (PINNs) are a class of deep learning models aiming to approximate solutions of PDEs by training neural networks to minimize the residual of the equation. Focusing on non-equilibrium fluctuating systems, we…

Machine Learning · Computer Science 2025-09-25 Javier Castro , Benjamin Gess

In this article, we propose a novel Stabilized Physics Informed Neural Networks method (SPINNs) for solving wave equations. In general, this method not only demonstrates theoretical convergence but also exhibits higher efficiency compared…

Numerical Analysis · Mathematics 2024-03-29 Yuling Jiao , Yuhui Liu , Jerry Zhijian Yang , Cheng Yuan

Physics-Informed Neural Networks (PINNs) present a transformative approach for smart grid modeling by integrating physical laws directly into learning frameworks, addressing critical challenges of data scarcity and physical consistency in…

Machine Learning · Computer Science 2025-09-01 Julen Cestero , Carmine Delle Femine , Kenji S. Muro , Marco Quartulli , Marcello Restelli

Physics-Informed Neural Networks (PINNs) solve partial differential equations using deep learning. However, conventional PINNs perform pointwise predictions that neglect dependencies within a domain, which may result in suboptimal…

Machine Learning · Computer Science 2025-05-26 Mayank Nagda , Phil Ostheimer , Thomas Specht , Frank Rhein , Fabian Jirasek , Stephan Mandt , Marius Kloft , Sophie Fellenz

The promise of ANNs to automatically discover and extract useful features/patterns from data without dwelling on domain expertise although seems highly promising but comes at the cost of high reliance on large amount of accurately labeled…