Publications

1. Zhang, Z., Dao, M., Karniadakis, G.E., Subresh, S., "Analyses of internal structures and defects in materials using physics-informed neural networks." Science Advances, (2022).

2. Goswami, S., Kontolati, K., Shields, M.D, Karniadakis, G.E., "Deep transfer operator learning for partial differential equations under conditional shift". Nature Machine Intelligence, (2022).

3. Zou, Z., Meng, X., Psaros, A.F., Karniadakis, G.E., "NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operations". arXiv:2208.1866v1. (2022)

4. Goswami, S., Yin, M., Yu, Y., Karniadakis, G.E., "A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials". Elsevier, Computer Methods in Applied Mechanics and Engineering. (2022).

5. Yu, J., Lu, L., Meng, X., Karniadakis, G.E., "Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems". Elsevier, Computer Methods in Applied Mechanics and Engineering. (2022)

6. Shukla, K., Xu, M., Trask, N., Karniadakis, G.E., "Scalable algorithms for physics-informed neural and graph networks". Cambridge University Press. (2022).

7. Lu, L., Meng, X., Cai, S., Mao, Z., Goswami, S., Zhang, Z., Karniadakis, G.E., "A comprehensive and fair comparison of two neural operators (with practical extension) based on FAIR data". Elsevier, Computer Methods in Applied Mechanics and Engineering. (2022).

8. Boster, K. A.S., Cai, S., Ladron-de-Guevara, A., Sun, J., Zheng, X., Du, T., Thomas, J.H., Nedergaard, M., Karniadakis, G.E., Kelley, D.H., "Artificial intelligence velocimetry reveals in vivo flow rates, pressure gradients, and shear stresses in murine perivascular flows". PNAS, (2023).

9. Zhu, M., Zhnag, H., Jiao, A., Karniadakis, G.E., Lu, L., "Reliable extrapolation of deep neural operators informed by physics or sparse observations". Elsevier, 2023.

10. M. de Hoop, D. Z. Huang, E. Qian, and A.M. Stuart; The Cost-Accuracy Trade-Off In Operator Learning With Neural Networks, Journal of Machine Learning 2022 1:3, 299-341. 

11. Jagtap, Ameya D., and George Em Karniadakis. "How important are activation functions in 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.

12. Yifan Chen, Houman Owhadi, Andrew M. Stuart, Consistency of Empirical Bayes And Kernel Flow For Hierarchical Parameter Estimation  (https://arxiv.org/abs/2005.11375, Math. Comp. 2021).  

13. Boumediene Hamzi, Romit Maulik, Houman Owhadi, Simple, low-cost, and accurate, data-driven geophysical forecasting with learned kernels. (https://arxiv.org/abs/2103.10935 Proceedings of the Royal Society A. 2021).

14. Jagtap, Ameya D., Zhiping Mao, Nikolaus Adams, and George Em Karniadakis. "Physics-informed neural networks for inverse problems in supersonic flows." Journal of Computational Physics 466 (2022): 111402. 

15. M Darcy, B Hamzi, G Livieri, H Owhadi, P Tavallali. One-shot learning of stochastic differential equations with data adapted kernels. Physica D: Nonlinear Phenomena 444, 133583. 2023

16. J Lee, E De Brouwer, B Hamzi, H Owhadi. Learning dynamical systems from data: A simple cross-validation perspective, part iii: Irregularly-sampled time series Physica D: Nonlinear Phenomena. Volume 443, January 2023, 133546 

17. H. Owhadi. Do ideas have shape? Idea registration as the continuous limit of artificial neural networks. Physica D: Nonlinear Phenomena 444, 133592, 2023. 

18. H Owhadi. Gaussian process hydrodynamics Applied Mathematics and Mechanics (English Edition), 2023 

19. M. E. Levine, A. M. Stuart; A Framework for Machine Learning of Model Error in Dynamical Systems, Comm. Amer. Math. Soc. 2 (2022), 283-344.

20. Chen, Yifan, Bamdad Hosseini, Houman Owhadi, and Andrew M. Stuart. "Solving and learning nonlinear PDEs with Gaussian processes." Journal of Computational Physics 447 (2021): 110668. 

21. Kovachki, Nikola, Burigede Liu, Xingsheng Sun, Hao Zhou, Kaushik Bhattacharya, Michael Ortiz, and Andrew Stuart. "Multiscale modeling of materials: Computing, data science, uncertainty and goal-oriented optimization." Mechanics of Materials 165 (2022): 104156. 

22. Owhadi, Houman. "Computational graph completion." Research in the Mathematical Sciences volume 9, Article number: 27 (2022).

23. Shukla, K., Jagtap, A. D., & Karniadakis, G. E. (2021). Parallel physics-informed neural networks via domain decomposition. Journal of Computational Physics, 447 (2021) 110683  [arXiv Link]

24. Ameya D. Jagtap, Yeonjong Shin, Kenji Kawaguchi, and George Em Karniadakis. "Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions."  Neurocomputing 468, 165-180, 2022. [arXiv Link]

25. Shukla, K., Jagtap, A. D., Blackshire, J. L., Sparkman, D., & Karniadakis, G. E. (2021). A physics-informed neural network for quantifying the microstructure properties of polycrystalline Nickel using ultrasound data. IEEE Signal Processing Magazine, 39 (1), 68-77, 2022.  [arXiv Link]

26. Darbon, Jérôme, Langlois, Gabriel P., Meng, Tingwei."Overcoming the curse of dimensionality for some Hamilton–Jacobi partial differential equations via neural network architectures. "Research in the Mathematical Sciences, vol. 7, no. 3, 2020.

27. Jerome Darbon and Tingwei Meng, On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton--Jacobi partial differential equations. Journal of Computational Physics, Volume 425, 15 January 2021, 109907.

28. Meng, X., Babaee, H., & Karniadakis, G. E. (2021). Multi-fidelity Bayesian neural networks: Algorithms and applications. Journal of Computational Physics, 438, 110361. 

29. L. Yang, X. Meng, G. E. Karniadakis, “B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data”, Journal of Computational Physics, Volume 425, (2021), 109913

30. S. Cai, Z. Wang, S. Wang, P. Perdikaris, G. E. Karniadakis, “Physics-Informed Neural Networks for Heat Transfer Problems” ASME. J. Heat Transfer, (2021), 143(6): 060801

31. S. Fang, R. M. Kirby, S. Zhe, “Bayesian Streaming Sparse Tucker Decomposition”, 37th Conference on Uncertainty in Artificial Intelligence (UAI 2021)

32.  Z. Wang, W. Xing, R. M. Kirby, S. Zhe, “Multi-Fidelity High-Order Gaussian Processes for Physical Simulation”, Proceedings of the 24th International Conference on Artificial Intelligence and Statistics (AISTATS) 2021, San Diego, California, USA. PMLR: Volume 130, (2021)

33. Y. Chen, B. Hosseini, H. Owhadi, AM. Stuart, Solving and Learning Nonlinear PDEs with Gaussian Processes. 2021. Journal of Computational Physics.

34. Y. Chen, H. Owhadi, A. M. Stuart, Consistency of Empirical Bayes And Kernel Flow For Hierarchical Parameter Estimation. Mathematics of Computation, 2021. 

35. B. Hamzi, R.  Maulik, H. Owhadi, Data-driven geophysical forecasting: Simple, low-cost, and accurate baselines with kernel methods. Proceedings of the Royal Society A. 2021

36. Psaros, A. F., Kawaguchi, K., & Karniadakis, G. E. Meta-learning PINN loss functions. JCP, 2022, arXiv preprint arXiv:2107.05544. [arXiv Link]

37. Meng, X., Yang, L., Mao, Z., Ferrandis, J. D. A., & Karniadakis, G. E. Learning Functional Priors and Posteriors from Data and Physics. JCP 2022.

38. Yifan Chen, Houman Owhadi, Andrew M. Stuart, Consistency of Empirical Bayes And Kernel Flow For Hierarchical Parameter Estimation   (https://arxiv.org/abs/2005.11375, Math.Comp. 2021).

39. Chen, Yifan, Bamdad Hosseini, Houman Owhadi, and Andrew M. Stuart, Solving and learning nonlinear PDEs with Gaussian processes; Journal of Computational Physics 447 (2021): 110668.

40. Kovachki, Nikola, Burigede Liu, Xingsheng Sun, Hao Zhou, Kaushik Bhattacharya, Michael, Ortiz, and Andrew Stuart; Multiscale modeling of materials: Computing, data science, uncertainty and goal-oriented optimization; Mechanics of Materials 165 (2022): 104156.

41. Owhadi, Houman, Computational graph completion; Research in the Mathematical Sciences volume 9, Article number: 27 (2022).

42. Shibo Li, Robert M. Kirby, and Shandian Zhe, “Decomposing Temporal High-Order Interactions via Latent ODEs”, Proceedings of The 39th International Conference on Machine Learning (ICML), 2022.

43. Shikai Fang, Akil Narayan, Robert M. Kirby, and Shandian Zhe, “Bayesian Continuous-Time Tucker Decomposition” (Long Talk), Proceedings of The 39th International Conference on Machine Learning (ICML), 2022.

44. Shibo Li, Jeff Phillips, Xin Yu, Robert M. Kirby, and Shandian Zhe, “Batch Multi-Fidelity Active Learning with Budget Constraints”, Proceedings of Thirty-SixthConference on Neural Information Processing Systems (NeurIPS), 2022.

45. Shibo Li, Zheng Wang, Robert M. Kirby, and Shandian Zhe, “Infinite-Fidelity Coregionalization for Physical Simulation”, Proceedings of Thirty-Sixth Conference on Neural Information Processing Systems (NeurIPS), 2022.

46. Michael Penwarden, Shandian Zhe, Akil Narayan, and Robert M. Kirby, “A Meta learning Approach for Physics-Informed Neural Networks (PINNs): Application to Parameterized PDEs”, Journal of Computational Physics, 2023 .

47. Shibo Li, Zheng Wang, Akil Narayan, Robert Kirby, and Shandian Zhe, “Meta-Learning with Adjoint Methods ”, Proceedings of The 26th International Conference on Artificial Intelligence and Statistics (AISTATS) , 2023.

48. Shibo Li, Michael Penwarden, Yiming Xu, Conor Tillinghast, Akil Narayan, Robert Kirby, and Shandian Zhe, “Meta Learning of Interface Conditions for Multi-Domain Physics-Informed Neural Networks”, Proceedings of The 40th International Conference on Machine Learning (ICML), 2023.

49. Zheng Wang, Wei Xing, Robert M. Kirby, and Shandian Zhe, “Multi-Fidelity High-Order Gaussian Processes for Physical Simulation”, Proceedings of The 24th International Conference on Artificial Intelligence and Statistics (AISTATS), 2021.

50. Shikai Fang, Robert. M. Kirby, and Shandian Zhe, “Bayesian Streaming Sparse TuckerDecomposition”, Proceedings of The 37th Conference on Uncertainty in ArtificialIntelligence (UAI), 2021. 

51. Aditi Krishnapriyan, Amir Gholami, Shandian Zhe, Robert M. Kirby, and Michael W.Mahoney, “Characterizing Possible Failure Modes in Physics-Informed Neural Networks”, Proceedings of Thirty-fifth Conference on Neural Information Processing Systems (NeurIPS), 2021.

52. Shibo Li, Robert M. Kirby, and Shandian Zhe, “Batch Multi-Fidelity BayesianOptimization with Deep Auto-Regressive Networks”, Proceedings of Thirty-fifth Conference on Neural Information Processing Systems (NeurIPS), 2021.

53. Michael Penwarden, Shandian Zhe, Akil Narayan, and Robert M. Kirby, “Multifidelity Modeling for Physics-Informed Neural Networks (PINNs)”, Journal of Computational Physics, 2022.

54. Shibo Li, Zheng Wang, Robert M. Kirby, and Shandian Zhe, “Deep Multi-Fidelity Active Learning of High-Dimensional Outputs”, Proceedings of The 25th International Conference on Artificial Intelligence and Statistics (AISTATS) , 2022.

55. Zheng Wang, Wei Xing, Robert M. Kirby, and Shandian Zhe, “Physics Informed Deep Kernel Learning”, Proceedings of The 25th International Conference on Artificial Intelligence and Statistics (AISTATS) , 2022. 

56. Da Long, Zheng Wang, Aditi Krishnapriyan, Robert M. Kirby, Shandian Zhe, and Michael W. Mahoney, “AutoIP: A United Framework to Integrate Physics into Gaussian Processes”, Proceedings of The 39th International Conference on Machine Learning (ICML), 2022.

57. G. Boncoraglio and C. Farhat, “Piecewise-Global Nonlinear Model Order Reduction for PDE-Constrained Optimization in High-Dimensional Parameter Spaces,” SIAM Journal on Scientific Computing, in press, 2022

58. J. Lorenzetti, A. McClellan, C. Farhat and M. Pavone, “Linear Reduced Order Model Predictive Control,” IEEE Transactions on Automatic Control, DOI

10.1109/TAC.2022.3179539 (2022)

59. R. Tezaur, F. Asad, and C. Farhat, “Robust and Globally Efficient Reduction of Parametric,Highly Nonlinear Computational Models and Real Time Online Performance,” ComputerMethods in Applied Mechanics and Engineering, Vol. 399, 115392 (2022)

60. A. McClellan, J. Lorenzetti, M. Pavone and C. Farhat, A Physics-Based Digital Twin forModel Predictive Control of Autonomous Unmanned Aerial Vehicle Landing,”Philosophical Transactions of the Royal Society A, Vol. 380, 20210204 (2022)

61. J. Barnett and C. Farhat, “Quadratic Approximation Manifold for Mitigating theKolmogorov Barrier in Nonlinear Projection-Based Model Order Reduction,” Journal ofComputational Physics, Vol. 464, 111348 (2022)

62.  F. Asad, P. Avery and C. Farhat, “A Mechanics-Informed Artificial Neural NetworkApproach in Data-Driven Constitutive Modeling,” International Journal for Numerical Methods in Engineering, Vol. 123, pp. 2738-2759 (2022)

63.  G. Boncoraglio and C. Farhat, “Active Manifold and Model Order Reduction to AccelerateMultidisciplinary Analysis and Optimization,” AIAA Journal, Vol. 59, pp. 4739-4753 (2021)

64. Meng, Xuhui, Zhicheng Wang, Dixia Fan, Michael S. Triantafyllou, and George Em Karniadakis. "A fast multi-fidelity method with uncertainty quantification for complex data correlations: Application to vortex-induced vibrations of marine risers." Computer Methods in Applied Mechanics and Engineering 386 (2021): 114212. 

65. Penwarden, Michael, Shandian Zhe, Akil Narayan, and Robert M. Kirby. "Multifidelity modeling for physics-informed neural networks (PINNs)." Journal of Computational Physics 451 (2022): 110844. 

66. Darbon, Jérôme, Peter M. Dower, and Tingwei Meng. "Neural network architectures using min-plus algebra for solving certain high-dimensional optimal control problems and Hamilton–Jacobi PDEs." Mathematics of Control, Signals, and Systems 35, no. 1 (2023): 1-44. 

67. Chen, Yifan, Bamdad Hosseini, Houman Owhadi, and Andrew M. Stuart. "Solving and learning nonlinear PDEs with Gaussian processes." Journal of Computational Physics 447 (2021): 110668. 

68. Jin, Pengzhan, Zhen Zhang, Ioannis G. Kevrekidis, and George Em Karniadakis. "Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks." IEEE Transactions on Neural Networks and Learning Systems (2022). 

69. Levine, Matthew, and Andrew Stuart. "A framework for machine learning of model error in dynamical systems." Communications of the American Mathematical Society 2, no. 07 (2022): 283-344. 

70. Lee, Jonghyeon, Edward De Brouwer, Boumediene Hamzi, and Houman Owhadi. "Learning dynamical systems from data: A simple cross-validation perspective, Part III: Irregularly-sampled time series." Physica D: Nonlinear Phenomena 443 (2023): 133546. 

71. Owhadi, Houman. "Computational graph completion." Research in the Mathematical Sciences 9, no. 2 (2022): 27. 

72. Dingle, Kamaludin, Pau Batlle, and Houman Owhadi. "Multiclass classification utilising an estimated algorithmic probability prior." Physica D: Nonlinear Phenomena 448 (2023): 133713. 

73. Alhazmi, Nahla, Yousef Ghazi, Mohammed N. Aldosari, Radek Tezaur, and Charbel Farhat. "Training a neural-network-based surrogate model for aerodynamic optimization using a gaussian process." In AIAA Scitech 2021 Forum, p. 0893. 2021. 

74. Azzi, Marie-Jo, Chady Ghnatios, Philip Avery, and Charbel Farhat. "Acceleration of a Physics-Based Machine Learning Approach for Modeling and Quantifying Model-Form Uncertainties and Performing Model Updating." Journal of Computing and Information Science in Engineering 23, no. 1 (2023): 011009. 

75. Shin, Y., Darbon, J., Karniadakis, G.E., "Accelerating gradient descent and Adam via fractional gradients". Elsevier, Neural Networks. (2023).

76. Kontolati, K., Goswami, S., Shields, M D, Karniadakis, G.E., "On the influence of over parameterization in manifold based surrogates and deep neural operators". Elsevier, Journal of Computational Physics. (2023).

1. Zhang, E., Kahana, A., Turkel, E., Ranade, R., Pathak, J., Karniadakis, G.E., "A Hybrid Iterative numerical Transferable Solver (HINTS) for PDEs Based on Deep Operator Network and Relaxation Methods". arXiv:2208.13273, (2022).

2. Liu, L., Nath, K., Cai. W., "A Causality-DeepONet for Causal Responses of Linear Dynamical Systems". arXiv:2209.08397. (2022).

3. Cao, Q., Goswami, S., Karniadakis, G.E., Chakraborty, S., "Deep neural operators can predict the real-time response of floating offshore structures under irregular waves". arXiv:2302.06667v1. (2023).

4. Zou, Z., Karniadakis, G.E., "L-Hydra: Multi-head physics-informed neutral networks". arXiv:2301.02152va. (2023).

5. Bajgiran, Hamed Hamze, and Houman Owhadi, Aggregation of Pareto optimal models; arXiv preprint arXiv:2112.04161, 2021.

6. Hamed Hamze Bajgiran, Houman Owhadi “Aggregation of Models, Choices, Beliefs, and Preferences.” arXiv:2111.11630, 2021.

7. Florian Schäfer, Houman Owhadi, Sparse recovery of elliptic solvers from matrix-vector products. arXiv:2110.05351

8. Shin, Y., Darbon, J., & Karniadakis, G. E. (2021). A Caputo fractional derivative-based algorithm for optimization. arXiv preprint arXiv:2104.02259. [arXiv Link]

9. Shin, Y., Zhang, Z., & Karniadakis, G. E. (2020). Error estimates of residual minimization using neural networks for linear PDEs. arXiv preprint arXiv:2010.08019.  [arXiv Link]

10. B. Hamzi, R. Maulik, H. Owhadi, “Data-driven geophysical forecasting: Simple, low-cost, and accurate baselines with kernel methods Boumediene”, 2103.10935, arXiv, physics.ao-ph, (2021), arXiv:2103.10935 

11.  L. Yang, T. Meng, G. E. Karniadakis, “Measure-conditional Discriminator with Stationary Optimum for GANs and Statistical Distance Surrogates”, ArXiv, (2021), abs/2101.06802

12. Matthieu Darcy, Boumediene Hamzi, Giulia Livieri, Houman Owhadi, Peyman Tavallali, One-Shot Learning of Stochastic Differential Equations with Computational Graph Completion. DOI: 10.13140/RG.2.2.32262.65604

13. Hamed Hamze Bajgiran, Houman Owhadi, Aggregation of Pareto optimal models. 2021. [arXiv:2112.04161]

14. Hamed Hamze Bajgiran, Houman Owhadi, Aggregation of Models, Choices, Beliefs, and Preferences. 2021. [arXiv:2111.11630]

15. M. Darcy, B. Hamzi, J. Susiluoto, A. Braverman, H. Owhadi, Learning dynamical systems from data: a simple cross-validation perspective, part II: nonparametric kernel flows. 

16. F. Schäfer, H. Owhadi, Sparse recovery of elliptic solvers from matrix-vector products. [arXiv:2110.05351]

17. L Yang, X Sun, B Hamzi, H Owhadi, N Xie. Learning Dynamical Systems from Data: A Simple Cross-Validation Perspective, Part V: Sparse Kernel Flows for Chaotic Dynamical Systems [ arXiv:2301.10321 ]

18. Y. Chen, D. Zhengyu Huang, J. Huang, S. Reich, A. M. Stuart; Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariance. arXiv:2302.11024, 2023.

19. T. Helin, A. Stuart, A. Teckentrup, K. Zygalakis; Introduction To Gaussian ProcessRegression In Bayesian Inverse Problems, With New Results On Experimental Design For Weighted Error Measures. arXiv:2302.04518

20. Michael Penwarden, Ameya D. Jagtap, Shandian Zhe, George Em. Karniadakis and Robert M. Kirby, “A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions”, Under Review, Journal of Computational Physics, 2023.

21. Shikai Fang, Madison Cooley, Shibo Li, Robert M. Kirby, and Shandian Zhe, “Solving High Frequency and Multi-Scale Problems with Gaussian Processes”, Under Review, Thirty-Seventh Conference Neural Information Processing Systems (NeurIPS), 2023.

22. Madison Cooley, Varun Shankar, Shandian Zhe, and Robert M. Kirby, “Polynomial- Enriched Physics-Informed Neural Networks”, Under Review, Thirty-Seventh Conference Neural Information Processing Systems (NeurIPS), 2023.

23. Da Long, Wei W. Xing, Aditi S. Krishnapriyan, Robert Kirby, Shandian Zhe, and Michael W. Mahoney, “Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernels”, Under Review, Thirty-Seventh Conference Neural Information Processing Systems (NeurIPS), 2023.

24. Pau Batlle , Yifan Chen, Bamdad Hosseini, Houman Owhadi, and Andrew M Stuart, Error Analysis of Kernel/GP Methods for Nonlinear and Parametric PDEs. arXiv:2305.04962.

25. Samuel Lanthaler, Zongyi Li, Andrew M. Stuart. The Nonlocal Neural Operator: Universal Approximation. arXiv:2304.13221   

26. Pau Batlle, Matthieu Darcy, Bamdad Hosseini, Houman Owhadi, Kernel Methods are Competitive for Operator Learning. arXiv:2304.13202.

27. Y. Chen, D. Zhengyu Huang, J. Huang, S. Reich, A. M. Stuart; Gradient Flows for Sampling: Mean-Field Models, Gaussian Approximations and Affine Invariance. arXiv:2302.11024

28. T. Helin, A. Stuart, A. Teckentrup, K. Zygalakis; Introduction To Gaussian Process Regression In Bayesian Inverse Problems, With New Results On Experimental Design For Weighted Error Measures. arXiv:2302.04518

29. Yifan Chen, Houman Owhadi, Florian Schäfer. Sparse Cholesky Factorization for Solving Nonlinear PDEs via Gaussian Processes. arXiv:2304.01294.

30. Shekarpaz, Simin, Fanhai Zeng, and George Karniadakis. "Splitting physics-informed neural networks for inferring the dynamics of integer-and fractional-order neuron models." arXiv preprint arXiv:2304.13205 (2023). 

31. Chen, Paula, Tingwei Meng, Zongren Zou, Jérôme Darbon, and George Em Karniadakis. "Leveraging Multi-time Hamilton-Jacobi PDEs for Certain Scientific Machine Learning Problems." arXiv preprint arXiv:2303.12928 (2023).

32. Hu, Zheyuan, Ameya D. Jagtap, George Em Karniadakis, and Kenji Kawaguchi. "Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology." arXiv preprint arXiv:2211.08939 (2022).