Relevant bibliographies by topics / Neural fields equations

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Neural fields equations'

Author: Grafiati
Published: 25 May 2024
Last updated: 31 July 2025

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Journal articles on the topic "Neural fields equations"

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Veltz, Romain, and Olivier Faugeras. "A Center Manifold Result for Delayed Neural Fields Equations." SIAM Journal on Mathematical Analysis 45, no. 3 (2013): 1527–62. http://dx.doi.org/10.1137/110856162.

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Belhe, Yash, Michaël Gharbi, Matthew Fisher, Iliyan Georgiev, Ravi Ramamoorthi, and Tzu-Mao Li. "Discontinuity-Aware 2D Neural Fields." ACM Transactions on Graphics 42, no. 6 (2023): 1–11. http://dx.doi.org/10.1145/3618379.

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Neural image representations offer the possibility of high fidelity, compact storage, and resolution-independent accuracy, providing an attractive alternative to traditional pixel- and grid-based representations. However, coordinate neural networks fail to capture discontinuities present in the image and tend to blur across them; we aim to address this challenge. In many cases, such as rendered images, vector graphics, diffusion curves, or solutions to partial differential equations, the locations of the discontinuities are known. We take those locations as input, represented as linear, quadra
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Scheinker, Alexander, and Reeju Pokharel. "Physics-constrained 3D convolutional neural networks for electrodynamics." APL Machine Learning 1, no. 2 (2023): 026109. http://dx.doi.org/10.1063/5.0132433.

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We present a physics-constrained neural network (PCNN) approach to solving Maxwell’s equations for the electromagnetic fields of intense relativistic charged particle beams. We create a 3D convolutional PCNN to map time-varying current and charge densities J(r, t) and ρ(r, t) to vector and scalar potentials A(r, t) and φ(r, t) from which we generate electromagnetic fields according to Maxwell’s equations: B = ∇ × A and E = −∇ φ − ∂A/ ∂t. Our PCNNs satisfy hard constraints, such as ∇ · B = 0, by construction. Soft constraints push A and φ toward satisfying the Lorenz gauge.
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Nicks, Rachel, Abigail Cocks, Daniele Avitabile, Alan Johnston, and Stephen Coombes. "Understanding Sensory Induced Hallucinations: From Neural Fields to Amplitude Equations." SIAM Journal on Applied Dynamical Systems 20, no. 4 (2021): 1683–714. http://dx.doi.org/10.1137/20m1366885.

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Veltz, Romain, and Olivier Faugeras. "ERRATUM: A Center Manifold Result for Delayed Neural Fields Equations." SIAM Journal on Mathematical Analysis 47, no. 2 (2015): 1665–70. http://dx.doi.org/10.1137/140962279.

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Bressloff, Paul C., and Zachary P. Kilpatrick. "Nonlinear Langevin Equations for Wandering Patterns in Stochastic Neural Fields." SIAM Journal on Applied Dynamical Systems 14, no. 1 (2015): 305–34. http://dx.doi.org/10.1137/140990371.

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Sim, Fabio M., Eka Budiarto, and Rusman Rusyadi. "Comparison and Analysis of Neural Solver Methods for Differential Equations in Physical Systems." ELKHA 13, no. 2 (2021): 134. http://dx.doi.org/10.26418/elkha.v13i2.49097.

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Differential equations are ubiquitous in many fields of study, yet not all equations, whether ordinary or partial, can be solved analytically. Traditional numerical methods such as time-stepping schemes have been devised to approximate these solutions. With the advent of modern deep learning, neural networks have become a viable alternative to traditional numerical methods. By reformulating the problem as an optimisation task, neural networks can be trained in a semi-supervised learning fashion to approximate nonlinear solutions. In this paper, neural solvers are implemented in TensorFlow for
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Dong, Chenghao. "Solving Differential Equations with Physics-Informed Neural Networks." Theoretical and Natural Science 87, no. 1 (2025): 137–46. https://doi.org/10.54254/2753-8818/2025.20346.

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Solving differential equations is an extensive topic in various fields, such as fluid mechanics and mathematical finance. The recent resurgence in deep neural networks has opened up a brand new track for numerically solving these equations, with the potential to better deal with nonlinear problems and overcome the curse of dimensionality. The Physics-Informed Neural Network (PINN) is one of the fundamental attempts to solve differential equations using deep learning techniques. This paper aims to briefly review the application of PINNs and their variants in solving differential equations throu
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ITOH, MAKOTO, and LEON O. CHUA. "IMAGE PROCESSING AND SELF-ORGANIZING CNN." International Journal of Bifurcation and Chaos 15, no. 09 (2005): 2939–58. http://dx.doi.org/10.1142/s0218127405013794.

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CNN templates for image processing and pattern formation are derived from neural field equations, advection equations and reaction–diffusion equations by discretizing spatial integrals and derivatives. Many useful CNN templates are derived by this approach. Furthermore, self-organization is investigated from the viewpoint of divergence of vector fields.
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Park, Yongsung, Seunghyun Yoon, Peter Gerstoft, and Woojae Seong. "Physics-informed neural network-based predictions of ocean acoustic pressure fields." Journal of the Acoustical Society of America 155, no. 3_Supplement (2024): A44. http://dx.doi.org/10.1121/10.0026740.

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Physics-informed neural network (PINN) trains the network using sampled data and encodes the underlying physical laws governing the dataset, such as partial differential equations (PDEs). A trained PINN can predict data at locations beyond the sampled data positions. The ocean acoustic pressure field satisfies PDEs, Helmholtz equations. We present a method utilizing PINN for predicting the underwater acoustic pressure field. Our approach trains the network by fitting sampled data, embedding PDEs, and enforcing pressure-release surface boundary conditions. We demonstrate our approach under vari
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Dissertations / Theses on the topic "Neural fields equations"

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Ueda, Hiroyuki. "Studies on low-field functional MRI to detect tiny neural magnetic fields." Doctoral thesis, Kyoto University, 2021. http://hdl.handle.net/2433/263666.

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付記する学位プログラム名: 京都大学卓越大学院プログラム「先端光・電子デバイス創成学」<br>京都大学<br>新制・課程博士<br>博士(工学)<br>甲第23205号<br>工博第4849号<br>京都大学大学院工学研究科電気工学専攻<br>(主査)教授 小林 哲生, 教授 松尾 哲司, 特定教授 中村 武恒<br>学位規則第4条第1項該当<br>Doctor of Philosophy (Engineering)<br>Kyoto University<br>DFAM
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Faye, Grégory. "Symmetry breaking and pattern formation in some neural field equations." Nice, 2012. http://www.theses.fr/2012NICE4017.

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Cette thèse se propose de comprendre la formation de structures dans les équations de champs neuronaux en présence de symétrie ainsi que la conséquence pour la modélisation du cortex visuel. Les équations de champs neuronaux sont des modèles mésoscopiques qui décrivent l'activité spatio-temporelle de populations de neurones. Elles ont été introduites dans les années 1970 et sont souvent appelées les équations de Wilson-Cowan-Amari en référence à leurs auteurs. D'un point de vue mathématique, les équations de champs neuronaux sont des équations intégro-différentielles posées sur des domaines qu
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ALMEIDA, Arthur Santos de. "Algumas propriedades de equações diferenciais em espaços de Banach e aplicações de campos neurais." Universidade Federal de Campina Grande, 2015. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1404.

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Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-08-10T17:51:03Z No. of bitstreams: 1 BRUNO ARTHUR SANTOS DE ALMEIDA - DISSERTAÇÃO PPGMAT 2015..pdf: 938463 bytes, checksum: ad040a3bd6379e6ea801856f1925dcca (MD5)<br>Made available in DSpace on 2018-08-10T17:51:03Z (GMT). No. of bitstreams: 1 BRUNO ARTHUR SANTOS DE ALMEIDA - DISSERTAÇÃO PPGMAT 2015..pdf: 938463 bytes, checksum: ad040a3bd6379e6ea801856f1925dcca (MD5) Previous issue date: 2015-08<br>Capes<br>Para ler o resumo deste trabalho recomendamos o download do arquivo, uma vez que o mesmo possui fórmulas e caracteres ma
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Wang, Wei 1974. "On solutions of advanced-retarded travelling wave equations arising in a neural field theory." Thesis, McGill University, 2006. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=98515.

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We consider a firing rate and a spike frequency adaptation (SFA) model of a one-dimensional neuronal network with axo-dendritic synaptic interactions. The neuronal network we focus on has a compactly supported connectivity pattern. The model equations are integro-differential equations with spatio-temporal delays arising from the finite axonal conduction velocity. We show that travelling wave solutions of these models are determined by mixed-type functional differential equations with both advanced and retarded delays. Especially, both delays depend on a unknown travelling wave speed. Based on
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Tamekue, Cyprien. "Controllability, Visual Illusions and Perception." Electronic Thesis or Diss., université Paris-Saclay, 2023. http://www.theses.fr/2023UPAST105.

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Cette thèse explore deux applications distinctes de la théorie du contrôle dans différents domaines scientifiques : la physique et les neurosciences. La première application se concentre sur la contrôlabilité nulle de l'équation parabolique associée à l'opérateur de Baouendi-Grushin sur la sphère de dimension 2. En revanche, la deuxième application concerne la description mathématique des illusions visuelles du type MacKay, et se focalise sur l'effet MacKay et les expériences psychophysiques de Billock et Tsou, via le contrôle de l'équation des champs neuronaux à une seule couche du type Amari
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SILVA, Michel Barros. "Comportamento Assintótico para Equação de Campos Neurais." Universidade Federal de Campina Grande, 2014. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1395.

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Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-08-09T17:18:23Z No. of bitstreams: 1 MICHEL BARROS SILVA - DISSERTAÇÃO PPGMAT 2014..pdf: 335576 bytes, checksum: f2ee6b6d68cdefa6c32e300154d28756 (MD5)<br>Made available in DSpace on 2018-08-09T17:18:23Z (GMT). No. of bitstreams: 1 MICHEL BARROS SILVA - DISSERTAÇÃO PPGMAT 2014..pdf: 335576 bytes, checksum: f2ee6b6d68cdefa6c32e300154d28756 (MD5) Previous issue date: 2014-02<br>Capes<br>Para ler o reumo deste trabalho recomendamos o download do arquivo, pois o mesmo possui fórmulas e caracteres matemáticos que não foram possív
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Vellmer, Sebastian. "Applications of the Fokker-Planck Equation in Computational and Cognitive Neuroscience." Doctoral thesis, Humboldt-Universität zu Berlin, 2020. http://dx.doi.org/10.18452/21597.

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In dieser Arbeit werden mithilfe der Fokker-Planck-Gleichung die Statistiken, vor allem die Leistungsspektren, von Punktprozessen berechnet, die von mehrdimensionalen Integratorneuronen [Engl. integrate-and-fire (IF) neuron], Netzwerken von IF Neuronen und Entscheidungsfindungsmodellen erzeugt werden. Im Gehirn werden Informationen durch Pulszüge von Aktionspotentialen kodiert. IF Neurone mit radikal vereinfachter Erzeugung von Aktionspotentialen haben sich in Studien die auf Pulszeiten fokussiert sind als Standardmodelle etabliert. Eindimensionale IF Modelle können jedoch beobachtetes Pul
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Daya, Bassam. "Résolution numérique des équations du champ neural : étude de la coordination du mouvement par des modèles mathématiques du cervelet." Angers, 1996. http://www.theses.fr/1996ANGE0013.

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Nous abordons le problème de la coordination du mouvement par les deux approches continues et discrètes, afin de les comparer en vue du neurocontrôle en robotique. Dans le premier chapitre, le formalisme des champs et les équations du champ pour un tissu nerveux ont été rappelés. Ces équations incluent les mécanismes physiologiques du système nerveux pour mieux tenir compte de la réalité. Les hypothèses permettant de retrouver les modèles classiques ont été déterminées, prouvant ainsi la généralité de la théorie du champ envisagée. Dans le deuxième chapitre, la résolution numérique des équatio
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Quininao, Cristobal. "Mathematical modeling in neuroscience : collective behavior of neuronal networks & the role of local homeoproteins diffusion in morphogenesis." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066152/document.

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Ce travail est consacré à l’étude de quelques questions issues de la modélisation des systèmes biologiques en combinant des outils analytiques et probabilistes. Dans la première partie, nous nous intéressons à la dérivation des équations de champ moyen associées aux réseaux de neurones, ainsi qu’à l’étude de la convergence vers l’équilibre des solutions. Dans le Chapitre 2, nous utilisons la méthode de couplage pour démontrer la propagation du chaos pour un réseau neuronal avec délais et avec une architecture aléatoire. Dans le Chapitre 3, nous considérons une équation cinétique du type FitzHu
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Костів, Б. В. "Удосконалення безкоштовного визначення струмів в стінках підземних трубопроводів для контролю їх ізоляційного покриття". Thesis, Івано-Франківський національний технічний університет нафти і газу, 2010. http://elar.nung.edu.ua/handle/123456789/1974.

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У дисертації розроблено спосіб безконтактного визначення струму в стінках одного підземного трубопроводу на основі однократного вимірювання напруженостей п’ятьма магнітними антенами, що знаходяться в двох блоках, без попередньої орієнтації бази вимірювальної системи в перпендикулярній до осі трубопроводу площині. Розроблено спосіб автоматичного профілювання горизонтальної складової напруженості магнітного поля при проходженні із вимірювачьною системою над трубопроводами в перпендикулярному відносно їх осей напрямку. Запропоновано використання трьохшарової нейронної мережі для безконтактного ви
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Books on the topic "Neural fields equations"

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Neural Fields: Theory and Applications. Springer, 2014.

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Potthast, Roland, P. Beim Graben, Wright James, and Stephen Coombes. Neural Fields: Theory and Applications. Springer Berlin / Heidelberg, 2016.

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Potthast, Roland, Wright James, Stephen Coombes, and Peter beim Graben. Neural Fields: Theory and Applications. Springer London, Limited, 2014.

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Waves In Neural Media From Single Neurons To Neural Fields. Springer-Verlag New York Inc., 2013.

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Wadman, Wytse J., and Fernando H. Lopes da Silva. Biophysical Aspects of EEG and MEG Generation. Edited by Donald L. Schomer and Fernando H. Lopes da Silva. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780190228484.003.0004.

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This chapter reviews the essential physical principles involved in the generation of electroencephalographic (EEG) and magnetoencephalographic (MEG) signals. The general laws governing the electrophysiology of neuronal activity are analyzed within the formalism of the Maxwell equations that constitute the basis for understanding electromagnetic fields in general. Three main topics are discussed. The first is the forward problem: How can one calculate the electrical field that results from a known configuration of neuronal sources? The second is the inverse problem: Given an electrical field as
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van Hinsbergh, Victor W. M. Physiology of blood vessels. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780198755777.003.0002.

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This chapter covers two major fields of the blood circulation: ‘distribution’ and ‘exchange’. After a short survey of the types of vessels, which form the circulation system together with the heart, the chapter describes how hydrostatic pressure derived from the heartbeat and vascular resistance determine the volume of blood that is locally delivered per time unit. The vascular resistance depends on the length of the vessel, blood viscosity, and, in particular, on the diameter of the vessel, as formulated in the Poiseuille-Hagen equation. Blood flow can be determined in vivo by different imagi
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Book chapters on the topic "Neural fields equations"

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Sun, Yuqiu, and Wei Xv. "Application of Physical Information Neural Network Based on Fourier Features in Electromagnetic Computing." In Lecture Notes in Electrical Engineering. Springer Nature Singapore, 2025. https://doi.org/10.1007/978-981-96-4856-6_6.

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Abstract In recent years, artificial intelligence technologies have been widely applied across various fields, demonstrating significant potential, particularly in scientific computing. This paper proposes a neural network approach based on Fourier features to solve partial differential equations (PDEs) related to electromagnetic physical laws, starting from the general solution form of PDEs. By integrating Physics-Informed Neural Networks (PINNs) with automatic differentiation techniques, a loss function is constructed based on PDEs and known conditions. The effectiveness and accuracy of this
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Helias, Moritz, and David Dahmen. "Functional Formulation of Stochastic Differential Equations." In Statistical Field Theory for Neural Networks. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-46444-8_7.

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Helias, Moritz, and David Dahmen. "Perturbation Theory for Stochastic Differential Equations." In Statistical Field Theory for Neural Networks. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-46444-8_9.

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Alecu, Lucian, and Hervé Frezza-Buet. "Application-Driven Parameter Tuning Methodology for Dynamic Neural Field Equations." In Neural Information Processing. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-10677-4_15.

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La Camera, Giancarlo. "The Mean Field Approach for Populations of Spiking Neurons." In Advances in Experimental Medicine and Biology. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89439-9_6.

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AbstractMean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural circuits, these parameters are typically the firing rates of distinct, homogeneous subgroups of neurons. Knowledge of the firing rates under conditions of interest can reveal essential information on both the dynamics of neural circuits and the way they can subserve brain function. The goal of this chapter is to provide an elementary introduction to the
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La Camera, Giancarlo. "The Mean Field Approach for Populations of Spiking Neurons." In Advances in Experimental Medicine and Biology. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89439-9_6.

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AbstractMean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural circuits, these parameters are typically the firing rates of distinct, homogeneous subgroups of neurons. Knowledge of the firing rates under conditions of interest can reveal essential information on both the dynamics of neural circuits and the way they can subserve brain function. The goal of this chapter is to provide an elementary introduction to the
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Lima, Pedro M. "Numerical Investigation of Stochastic Neural Field Equations." In Advances in Mechanics and Mathematics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-02487-1_2.

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Takabe, Hideaki. "Basic Properties of Plasma in Fluid Model." In Springer Series in Plasma Science and Technology. Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-45473-8_2.

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AbstractIf the spatial variation of plasma is longer than the particle mean free path and the time variation is sufficiently longer than the plasma Coulomb collision time, the plasma can be approximated as being in local thermal equilibrium (LTE) at any point (t, r). Then the velocity distribution functions of the particles become Maxwellian. In addition, assuming Maxwellian is also a good assumption in many cases even for collisionless plasmas such as high-temperature fusion plasmas. In the fluid model of plasmas, The plasmas can be described in terms of five variables characterizing local Ma
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Burlakov, Evgenii, Vitaly Verkhlyutov, Ivan Malkov, and Vadim Ushakov. "Assessment of Cortical Travelling Waves Parameters Using Radially Symmetric Solutions to Neural Field Equations with Microstructure." In Advances in Neural Computation, Machine Learning, and Cognitive Research IV. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-60577-3_5.

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Takabe, Hideaki. "Non-local Transport of Electrons in Plasmas." In Springer Series in Plasma Science and Technology. Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-45473-8_6.

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AbstractSince plasma is high temperature and the charge particles are running with high temperature, for example, at 1 keV, about the velocity of 109 (electron) and 2 × 107 (ion) [cm/s]. Since Coulomb mean-free-path is proportional to (velocity)4, higher velocity component transfers its energy over a long distance without Coulomb collision. This is usually called as “non-local transport” and the traditional diffusion model in neutral gas cannot be applicable. In laser plasma, the locally heated electron thermal energy is transported into cold over-dense region non-locally. The best way to solv
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Conference papers on the topic "Neural fields equations"

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Lin, Wei-Shiang, Yi-Hsiang Cheng, Zhen-Yu Hung, and Yuan Yao. "Developing a Digital Twin System Based on a Physics-informed Neural Network for Pipeline Leakage Detection." In The 35th European Symposium on Computer Aided Process Engineering. PSE Press, 2025. https://doi.org/10.69997/sct.126840.

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As the demand for resources continues to grow, pipelines have become critical for transporting water, fossil fuels, and chemicals. Monitoring pipeline systems is essential, as leaks can lead to severe environmental damage and safety hazards. This study aims to develop a pipeline leakage detection system based on digital twin technology and Physics-Informed Neural Networks (PINNs). By embedding physical principles, such as the continuity and momentum equations derived from the Navier-Stokes equation, into the neural network's loss function, the model can predict pressure and flow dynamics with
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Moreno-Palancas, Isabela Fons, Raquel Salcedo D�az, Rub�n Ruiz Femenia, and Jos� A. Caballero. "Optimal Design and Control of Chemical Reactors using PINN-based frameworks." In The 35th European Symposium on Computer Aided Process Engineering. PSE Press, 2025. https://doi.org/10.69997/sct.140730.

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In an era defined by economic competitiveness and environmental awareness, engineering solutions must maximize profitability, efficiency and sustainability, underscoring the relevance of process optimization and the societal impact any contribution in this research field would bring. In chemical reactor engineering, optimization tasks pose significant challenges due to the highly non-linear and non-convex nature of reactor models, often involving differential equations. While conventional approaches have proven to be reliable strategies for solving these complex problems, their application bec
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Yan, Chang, Shengjun Ju, Dilong Guo, Guowei Yang, and Shuanbao Yao. "Inferring Unsteady Wake Flow Fields From Partial Data by Physics-Informed Neural Networks." In ASME 2022 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/fedsm2022-86945.

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Abstract Massive differential numerical computations are necessary in Computational Fluid Dynamics. In addition, the experimental results are generally noisy. Consequently, traditional methods cannot get unsteady flow fields immediately and precisely. In this research, the inferences of unsteady wake flow fields at different Reynolds numbers by Physics-Informed Neural Networks (PINNs) are studied. Unlike typical neural networks whose loss function consists of Mean Square Error only, the loss function of PINNs consists of Mean Square Error and the sum of squares of residuals of the flow governi
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Jo, Minju, Seungji Kook, and Noseong Park. "Hawkes Process Based on Controlled Differential Equations." In Thirty-Second International Joint Conference on Artificial Intelligence {IJCAI-23}. International Joint Conferences on Artificial Intelligence Organization, 2023. http://dx.doi.org/10.24963/ijcai.2023/239.

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Hawkes processes are a popular framework to model the occurrence of sequential events, i.e., occurrence dynamics, in several fields such as social diffusion. In real-world scenarios, the inter-arrival time among events is irregular. However, existing neural network-based Hawkes process models not only i) fail to capture such complicated irregular dynamics, but also ii) resort to heuristics to calculate the log-likelihood of events since they are mostly based on neural networks designed for regular discrete inputs. To this end, we present the concept of Hawkes process based on controlled differ
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Hu, Hao, Sheng Fang, Xinwen Dong, Yuhan Xu, and Shuhan Zhuang. "Reconstruction of Complex Scene Radiation Fields Based on Image Restoration Equation." In 2024 31st International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2024. http://dx.doi.org/10.1115/icone31-135542.

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Abstract In the context of nuclear safety production, the detailed information on three-dimensional radiation field dose rates plays a vital role in enhancing radiation protection and planning for radioactive areas. Research on inversion methods, especially under scenarios of sparse or irregular measurement points, has attracted significant attention. Currently, there are advances in inversion methods based on interpolation algorithms and neural network techniques. Interpolation algorithms are inversion methods capable of rapidly inverting and reconstructing the distribution of radiation field
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Zhang, Chi, Shihao Wang, and Yu-Shu Wu. "A Physics-Informed Neural Network for Temporospatial Prediction of Hydraulic-Geomechanical Processes." In SPE Reservoir Simulation Conference. SPE, 2023. http://dx.doi.org/10.2118/212202-ms.

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Abstract This work aims to quantify the temporal and spatial evolution of pressure and stress fields in poroelastic reservoirs by replacing the conventional reservoir-geomechanical simulators with a novel convolutional-recurrent network (CNN-RNN) proxy. The proposed convolutional-recurrent neural network uses the governing equations of the coupled hydraulic-geomechanical process as the loss function. Initial conditions and spatial rock property fields are taken as inputs to predict the variation of pressure and stress fields. A customized convolutional filter mimicking the higher-order finite
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Shu, Jin, Guoqing Han, Zhenduo Yue, et al. "Enhancing Wellbore Transient Multiphase Flow Simulation with a Surrogate Model Utilizing Neural Differential Equations." In SPE Advances in Integrated Reservoir Modelling and Field Development Conference and Exhibition. SPE, 2025. https://doi.org/10.2118/225297-ms.

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Abstract Transient multiphase flow in wellbores is crucial for the production of oil and gas wells, impacting key areas such as gas well liquid loading prediction, hydrate development, as well as safe operation and risk management. Currently, traditional wellbore flow simulation relies heavily on commercial software like OLGA, which, although powerful, is predominantly based on numerical methods, thus resulting in high computational costs and slow response times. In the context of the rapid development of digital twin technology, this mode of simulation can no longer meet the needs for real-ti
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Post, Pascal, Benjamin Winhart, and Francesca di Mare. "Investigation of Physics-Informed Neural Networks Based Solution Techniques for Internal Flows." In ASME Turbo Expo 2022: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/gt2022-80960.

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Abstract In this work, we explore for the first time the possibility and potentials of employing the emerging PINNs approach in internal flow configurations, solving the steady state Euler equations in two dimensions for forward and inverse problems. In addition to a simple bump test case, the PINNs results of a highly loaded transonic linear turbine guide vane cascade are presented. For forward problems, we investigate different formulations of the transport equations and boundary conditions. Overall, PINNs approximate the solution with acceptable accuracy; however, conventional CFD methods a
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Wu, Yuliang, Fenglei Han, Xiao Peng, Liangtian Gao, Yiming Zhao, and Jiawei Zhang. "Research on a Fast Resistance Performance Prediction Method for SUBOFF Model Based on Physics-Informed Neural Networks (PINNs)." In ASME 2024 43rd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2024. http://dx.doi.org/10.1115/omae2024-126300.

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Abstract Physics-Informed Neural Networks (PINNs) represent a novel intelligent algorithm for solving partial differential equations (PDEs), which has been partially validated in solving Navier-Stokes equations. However, numerous challenges remain in the application of PINNs to the calculation of hydrodynamic performance of ships. This paper utilizes discrete solutions of the Navier-Stokes (N-S) equations obtained via the Finite Volume Method (FVM) and Reynolds Averaged Navier-Stokes (RANS) approach of the CFD method for training PINNs to directly solve flow field information. This approach ac
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Wei, Ping, Menghan Liu, Jianhuan Cen, Ziyang Zhou, Liao Chen, and Qingsong Zou. "PDENNEval: A Comprehensive Evaluation of Neural Network Methods for Solving PDEs." In Thirty-Third International Joint Conference on Artificial Intelligence {IJCAI-24}. International Joint Conferences on Artificial Intelligence Organization, 2024. http://dx.doi.org/10.24963/ijcai.2024/573.

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The rapid development of neural network (NN) methods for solving partial differential equations (PDEs) has created an urgent need for evaluation and comparison of these methods. In this study, we propose PDENNEval, a comprehensive and systematic evaluation of 12 NN methods for PDEs. These methods are classified into function learning type and operator learning type based on their different mathematical foundations. The evaluation is implemented using a diverse dataset comprising 19 distinct PDE problems selected from various scientific fields such as fluid, materials, finance, and electromagne
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Reports on the topic "Neural fields equations"

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Warrick, Arthur W., Gideon Oron, Mary M. Poulton, Rony Wallach, and Alex Furman. Multi-Dimensional Infiltration and Distribution of Water of Different Qualities and Solutes Related Through Artificial Neural Networks. United States Department of Agriculture, 2009. http://dx.doi.org/10.32747/2009.7695865.bard.

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The project exploits the use of Artificial Neural Networks (ANN) to describe infiltration, water, and solute distribution in the soil during irrigation. It provides a method of simulating water and solute movement in the subsurface which, in principle, is different and has some advantages over the more common approach of numerical modeling of flow and transport equations. The five objectives were (i) Numerically develop a database for the prediction of water and solute distribution for irrigation; (ii) Develop predictive models using ANN; (iii) Develop an experimental (laboratory) database of
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