Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs | Paper Citation Record

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This paper cites and Bengio, Y., 2016.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Bengio, Y., 2016

Reference 1

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This paper cites and Nasrabadi, N.M., 2006.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Nasrabadi, N.M., 2006

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This paper cites and Bishop, H., 2023.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Bishop, H., 2023

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This paper cites Neural networks and deep learning (Vol.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Neural networks and deep learning (Vol

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Linear algebra and learning from data (Vol

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This paper cites Understanding deep learning requires rethinking generalization.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Understanding deep learning requires rethinking generalization

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This paper cites and Kress, R., 1999.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Kress, R., 1999

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This paper cites and Silverman, H., 2006.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Silverman, H., 2006

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This paper cites and Shanahan, P., 2009.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Shanahan, P., 2009

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This paper cites and Savitha, R., 2013.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Savitha, R., 2013

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This paper cites On Complex Valued Convolutional Neural Networks.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs On Complex Valued Convolutional Neural Networks

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This paper cites Theory and Implementation of Complex-Valued Neural Networks.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Theory and Implementation of Complex-Valued Neural Networks

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Complex-valued Neural Networks -- Theory and Analysis

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This paper cites and Gao, S., 2022.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Gao, S., 2022

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This paper cites A Survey of Complex-Valued Neural Networks.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs A Survey of Complex-Valued Neural Networks

Reference 15

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This paper cites and Pernkopf, F., 2021, May.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Pernkopf, F., 2021, May

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Unresolved cited work

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Lee, K., 2018, September

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This paper cites and Weidmann, U., 2014.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Weidmann, U., 2014

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This paper cites Deep Complex Networks.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Deep Complex Networks

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This paper cites Complex-valued neural networks.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Complex-valued neural networks

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This paper cites Neuronal Synchrony in Complex-Valued Deep Networks.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Neuronal Synchrony in Complex-Valued Deep Networks

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This paper cites Solving the XOR problem and the detection of symmetry using a single complex-valued neuron.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Solving the XOR problem and the detection of symmetry using a single complex-valued neuron

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This paper cites On the inherent property of the decision boundary in complex-valued neural networks.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs On the inherent property of the decision boundary in complex-valued neural networks

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This paper cites An analysis of the fundamental structure of complex-valued neurons.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs An analysis of the fundamental structure of complex-valued neurons

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Complex-valued neural networks: Advances and applications [book review]

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Appendix a: Wirtinger calculus

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This paper cites Zur formalen theorie der funktionen von mehr komplexen veränderlichen.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Zur formalen theorie der funktionen von mehr komplexen veränderlichen

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Hirose, A., 2013

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Murase, K., 2011, November

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Comprehensive Survey of Complex-Valued Neural Networks: Insights into Backpropagation and Activation Functions

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Journal of Computational physics, 378, pp.686-707

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Yang, L., 2021

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Piccialli, F., 2022

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Karniadakis, G.E., 2020

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Wang, J.X., 2020

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Unresolved cited work

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Karniadakis, G.E., 2021

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Perdikaris, P., 2020

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Unresolved cited work

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Perdikaris, P., 2019

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Journal of computational physics, 394, pp.56-81

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Journal of Computational Physics, 425, p.109913

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs andE,W., 2018.Solving high-dimensionalpartialdifferential equationsusing deeplearning.Proceedings oftheNational Academy of Sciences, 115(34), pp.8505-8510

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Unresolved cited work

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Tchelepi, H.A., 2020

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Mahoney, M.W., 2021

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Perdikaris, P., 2021

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Perdikaris, P., 2022

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Courville, A., 2019, May

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Towards Understanding the Spectral Bias of Deep Learning

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Ng, R., 2020

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Kritchman, S., 2020, November

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Hongler, C., 2018

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Braga-Neto, U.M., 2023

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Unresolved cited work

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Ghosh, S., 2022

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Journal of Fluids and Structures, 139, p.104421

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Liu, L., 2026

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs A Simple but Efficient Transformer-Based Physics-Informed Neural Network for Incompressible Navier--Stokes Equations

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs arXiv preprint arXiv:2601.18848

Reference 62

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Lu, L., 2023

Reference 63

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Observation a8b190b8-d5ac-475a-a1fe-5276d7d7d256 · outbound

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Adam: A Method for Stochastic Optimization

Reference 64

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Nocedal, J., 1989

Reference 65

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This paper cites and Xia, Z., 2026.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Xia, Z., 2026

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-02T00:14:59.538943Z

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Popa, C.A., 2026

Reference 67

Resolution: unresolved; no resolver link, observed 2026-08-02T00:14:59.543050Z

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Observation 527b3742-e736-4cee-8040-98884bfb8f8f · outbound

This paper cites Physical Review Research, 7(1), p.013164.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Physical Review Research, 7(1), p.013164

Reference 68

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Observation a2e547a1-77e2-4d4c-a95e-0b90121ce280 · outbound

This paper cites IEEE transactions on neural networks, 18(5), pp.1280-1293.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs IEEE transactions on neural networks, 18(5), pp.1280-1293

Reference 69

Resolution: unresolved; no resolver link, observed 2026-08-02T00:14:59.551746Z

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Koutsougeras, C., 1992

Reference 70

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Observation c9ae98d3-c5c8-4293-bae1-1857eed5bf54 · outbound

This paper cites Proposal of fully complex-valued neural networks.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Proposal of fully complex-valued neural networks

Reference 71

Resolution: unresolved; no resolver link, observed 2026-08-02T00:14:59.560913Z

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Wright, S.J., 2006

Reference 72

Resolution: unresolved; no resolver link, observed 2026-08-02T00:14:59.565967Z

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Observation c262b120-05cf-496f-ab57-399e38bd7bab · outbound

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Karniadakis, G.E., 2021

Reference 73

Resolution: unresolved; no resolver link, observed 2026-08-02T00:14:59.570666Z

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Observation 27c34cad-367c-4492-a5a2-b1a30f5163c7 · outbound

This paper cites The Korteweg-de Vries equation and water waves.

Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs The Korteweg-de Vries equation and water waves

Reference 74

Resolution: unresolved; no resolver link, observed 2026-08-02T00:14:59.574792Z

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Observation 96d9ae35-dd23-42a0-a852-fa1cd743eaee · outbound

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs Unresolved cited work

Reference 75

Resolution: unresolved; no resolver link, observed 2026-08-02T00:14:59.579208Z

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Split Complex-Valued Physics-Informed Neural Networks for Forward and Inverse Nonlinear PDEs and Pons, J.A., 2025

Reference 76

Resolution: unresolved; no resolver link, observed 2026-08-02T00:14:59.583451Z

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