Publications

Journal Papers

Published

1. A. Peyvan, V. Oommen, Ameya D. Jagtap, G. E. Karniadakis,  RiemannONets: Interpretable Neural Operators for Riemann Problems, Computer Methods in Applied Mechanics and Engineering, Volume 426, 116996 (2024) [Journal] [arXiv] 

2. T. Kossaczka, Ameya D. Jagtap, Matthias Ehrhardt, Deep smoothness WENO scheme for two-dimensional hyperbolic conservation laws: A deep learning approach for learning smoothness indicators, Physics of Fluids 36, 036603 (2024) [Journal] 

3. S. Goswami, Ameya D. Jagtap, H. Babaee, B. T. Susi, and G.E. Karniadakis, Learning stiff chemical kinetics using extended deep neural operators, Computer Methods in Applied Mechanics and Engineering, Volume 419 (2024) 116674. [Journal] [arXiv]

4. Z. Hu, Ameya D. Jagtap, G. E. Karniadakis, K. Kawaguchi,  Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology. Engineering Applications of Artificial Intelligence, Volume 126  (2023) 107183.  [Journal] [arXiv]

5. M. Penwarden, Ameya D. Jagtap, S. Zhe, G.E.Karniadakis, M. Kirby, A unified scalable framework for causal sweeping strategies for physics-informed neural networks (PINNs) and their temporal decompositions, Journal of Computational Physics, Volume 493 (2023) 112464 [Journal] [arXiv]

(A unified framework for causality-enforcing PINNs with efficient temporal decompositions.) 

6. Ameya D. Jagtap, G.E. Karniadakis, How important are activation functions for regression and classification? A survey, performance comparison, and future directions, Journal of Machine Learning for Modeling and Computing, Volume 4, Issue 1, 2023, pp. 21-75  [Journal][arXiv]

(The first comprehensive survey of activation functions for both classification and regression problems)

7. T. De Ryck, Ameya D.  Jagtap, and S. Mishra, Error estimates for physics informed neural networks approximating the Navier-Stokes equations, IMA Journal of Numerical Analysis, Oxford Academic, 2023.  https://doi.org/10.1093/imanum/drac085 [Journal] [arXiv]

(First Nonlinear Theory for PINNs and XPINNs: This is the  first comprehensive theoretical analysis of PINNs (and XPINNs) for a prototypical nonlinear PDE, the Navier-Stokes equations.)

8. Ameya D. Jagtap, Z. Mao, N. Adams, G.E. Karniadakis, Physics-informed neural networks for inverse problems in supersonic flows,  Journal of Computational Physics, 466 (2022) 111402. [Journal] [arXiv]

9. Z. Hu, Ameya D. Jagtap, G. E. Karniadakis, K. Kawaguchi,  When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?,  SIAM Journal on Scientific Computing, Vol. 44, No. 5, pp. A3158–A3182. [Journal] [arXiv]

10. Ameya D. Jagtap, D. Mitsotakis, G. E. Karniadakis, Deep learning of inverse water waves problems using multi-fidelity data:  Application to Serre-Green-Naghdi equations, Ocean Engineering, 248 (2022) 110775.  [Journal] [arXiv]

11. Ameya D. Jagtap, Y. Shin, K. Kawaguchi, G. E. Karniadakis, Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions, Neurocomputing, Vol. 468, (2022), 165-180. [Journal] [arXiv] 

12. K. Shukla, Ameya D. Jagtap, James L. Blackshire, Daniel Sparkman, and G. E. Karniadakis, A physics-informed neural network for quantifying the microstructure properties of polycrystalline Nickel using ultrasound data, IEEE Signal Processing Magazine, vol. 39, no. 1, pp. 68-77, Jan. 2022.  [Journal] [arXiv]

13. K. Shukla, Ameya D. Jagtap, G. E. Karniadakis, Parallel Physics-Informed Neural Networks via Domain Decomposition, Journal of Computational Physics, 447 (2021) 110683. [Journal] [arXiv]

14. Ameya D. Jagtap, G. E. Karniadakis, Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition based Deep Learning Framework for Nonlinear Partial Differential Equations, Communications in Computational Physics, Vol. 28, No. 5, pp. 2002-2041, 2020. [Journal]

15. Ameya D. Jagtap, R. Kumar, Kinetic theory based multi-level finite difference WENO schemes for compressible Euler equations, Wave Motion, Vol. 98, November 2020, 102626. [Journal]

16. Ameya D. Jagtap, K. Kawaguchi, G. E. Karniadakis, Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 476: 20200334, 2020. [Journal] [arXiv]

17. Ameya D. Jagtap, E. Kharazmi, G. E. Karniadakis, Conservative Physics-Informed Neural Networks on Discrete Domains for Conservation Laws: Applications to forward and inverse problems, Computer Methods in Applied Mechanics and Engineering, 365 (2020) 113028. [Journal]

18. S. Rathan, R. Kumar, Ameya D. Jagtap, L1-type smoothness indicators based WENO scheme for nonlinear degenerate parabolic equations, Applied Mathematics and Computation, 375 (2020) 125112. [Journal]

19. Ameya D. Jagtap, K. Kawaguchi, G. E. Karniadakis,  Adaptive activation functions accelerate convergence in deep and physics-informed neural networks, Journal of Computational Physics, 404 (2020) 109136. [Journal][arXiv]

20. Z. Mao,  Ameya D. Jagtap, G. E. Karniadakis, Physics-Informed Neural Networks for high-speed flows, Computer Methods in Applied Mechanics and Engineering, 360 (2020) 112789. [Journal]

21. Ameya D. Jagtap, On spatio-temporal dynamics of sine-Gordon soliton in nonlinear non-homogeneous media using fully implicit spectral element scheme, Applicable Analysis, 100 : 1, 37-60, 2021. DOI: 10.1080/00036811.2019.1588961  [Journal]

22. Ameya D. Jagtap, A. S. V. Murthy, Higher order spectral element scheme for two- and three-dimensional Cahn-Hilliard equation, International Journal of Advances in Engineering Sciences and Applied Mathematics, Vol. 10, Issue 1, 79 - 89, 2018. [Journal]

23. Ameya D. Jagtap, A. S. V. Murthy, Higher order scheme for two-dimensional inhomogeneous Sine-Gordon equation with impulsive forcing, Communications in Nonlinear Science and Numerical Simulation, 64, 178-197, 2018.  [Journal]

24. Ameya D. Jagtap, Method of relaxed streamlined-upwinding for hyperbolic conservation laws, Wave Motion, 78, 132-161, 2018. [Journal] [arXiv]

25. M Saravanan, Ameya D. Jagtap,  A. S. V. Murthy, Perturbed soliton and director deformation in a ferronematic liquid crystal, Chaos, Solitons & Fractals, 106, 220-226, 2018. [Journal]

26. Ameya D. Jagtap, E. Saha, J.D. George, A. S. V. Murthy, Revisiting the inhomogeneously driven Sine-Gordon equation, Wave Motion, 73, 76-85, 2017. [Journal]

Submitted

27. S. Brahmachary, S. Joshi, A. Panda, K. Koneripalli, A. Sagotra, H. Patel, A. Sharma, Ameya D. Jagtap, Kaushic K, Large Language Model-Based Evolutionary Optimizer: Reasoning with elitism, arXiv preprint,  arXiv:2403.02054, 2024 [arXiv]

Conference proceedings

1. Ameya D. Jagtap and G E Karniadakis, Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations,  Proceedings of AAAI 2021 Spring Symposium on Combining Artificial Intelligence and Machine Learning in Physics  Sciences, Stanford University, CA, USA  (March 22nd - 24th, 2021).

2. Ameya D. Jagtap, Higher order scheme for Sine-Gordon Equation in Nonlinear Non-homogeneous Media, Proceedings of International Conference on Hyperbolic Equation: Theory and Numerics, (HYP2018), June 25-29, 2018, University Park, Pennsylvania, USA.  [Book]

3. Ameya D. Jagtap, Reinvestigating Discrete Stability of Numerical Scheme using Pseudospectra, Proceedings of 19th Annual AeSI CFD Symposium, August 10-11, 2017, National Aerospace Laboratory (NAL), Bangalore. India.

4. Ameya D. Jagtap, Method of Kinetic Streamline Upwinding and its Variant for Ideal Magnetohydrodynamics, Proceedings of 18th Annual AeSI CFD Symposium, August 10-11, 2016, National Aerospace Laboratory (NAL), Bangalore. India.

5. Ameya D. Jagtap, Modified Kinetic Streamline Upwind Petrov Galerkin Method for Euler Equations of Gas Dynamics, Proceedings of Sixth International Congress on Computational Mechanics and Simulation (ICCMS2016), IIT-Bombay, Mumbai, India, 27th June-1st July 2016.