Publications

1. Bodnar, C., Bruinsma, W. P., Lucic, A., Stanley, M., Brandstetter, J., Garvan, P., Riechert, M., Weyn, J., Dong, H., Vaughan, A., Gupta, J. K., Tambiratnam, K., Archibald, A., Heider, E., Welling, M., Turner, R. E., & Perdikaris, P. (2024). Aurora: A foundation model of the atmosphere. ArXiv Preprint ArXiv:2405.13063.
2. Wang, S., Seidman, J. H., Sankaran, S., Wang, H., Pappas, G. J., & Perdikaris, P. (2024). Bridging Operator Learning and Conditioned Neural Fields: A Unifying Perspective. ArXiv Preprint ArXiv:2405.13998.
3. Guilhoto, L. F., & Perdikaris, P. (2024). Composite Bayesian Optimization In Function Spaces Using NEON–Neural Epistemic Operator Networks. ArXiv Preprint ArXiv:2404.03099.
4. Guilhoto, L. F., & Perdikaris, P. (2024). Deep Learning Alternatives of the Kolmogorov Superposition Theorem. ArXiv Preprint ArXiv:2410.01990.
5. Guilhoto, L. F., & Perdikaris, P. (2024). Deep Learning Alternatives of the Kolmogorov Superposition Theorem. ArXiv e-Prints.
6. Mao, S., Dong, R., Yi, K. M., Lu, L., Wang, S., & Perdikaris, P. (2024). Disk2Planet: A Robust and Automated Machine Learning Tool for Parameter Inference in Disk-Planet Systems. ArXiv Preprint ArXiv:2409.17228.
7. Bergamin, F., Diaconu, C., Shysheya, A., Perdikaris, P., Hernández-Lobato, J. M., Turne, R. E., & Mathieu, E. (2024). Guided autoregressive diffusion models with applications to PDE simulation.
8. Fang, Z., Wang, S., & Perdikaris, P. (2024). Learning only on boundaries: a physics-informed neural operator for solving parametric partial differential equations in complex geometries. Neural Computation.
9. Wang, S., Liu, T.-R., Sankaran, S., & Perdikaris, P. (2024). Micrometer: Micromechanics Transformer for Predicting Mechanical Responses of Heterogeneous Materials. ArXiv Preprint ArXiv:2410.05281.
10. Lippe, P., Veeling, B., Perdikaris, P., Turner, R., & Brandstetter, J. (2024). Pde-refiner: Achieving accurate long rollouts with neural pde solvers. Advances in Neural Information Processing Systems.
11. Raissi, M., Perdikaris, P., Ahmadi, N., & Karniadakis, G. E. (2024). Physics-informed neural networks and extensions. ArXiv Preprint ArXiv:2408.16806.
12. Wang, S., Li, B., Chen, Y., & Perdikaris, P. (2024). PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks. ArXiv Preprint ArXiv:2402.00326.
13. Wang, S., Sankaran, S., & Perdikaris, P. (2024). Respecting causality for training physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering.
14. Liao, X., Qin, A., Seidman, J., Wang, J., Wang, W., & Perdikaris, P. (2024). Score Neural Operator: A Generative Model for Learning and Generalizing Across Multiple Probability Distributions. ArXiv Preprint ArXiv:2410.08549.
15. Costabal, F. S., Pezzuto, S., & Perdikaris, P. (2024). Δ-PINNs: physics-informed neural networks on complex geometries. Engineering Applications of Artificial Intelligence.
16. Wu, J., Wang, S. F., & Perdikaris, P. (2023). A dive into spectral inference networks: improved algorithms for self-supervised learning of continuous spectral representations. Applied Mathematics and Mechanics.
17. Mo, C., Perdikaris, P., & Raney, J. R. (2023). Accelerated design of architected materials with multifidelity Bayesian optimization. Journal of Engineering Mechanics.
18. Wang, S., Sankaran, S., Wang, H., & Perdikaris, P. (2023). An expert’s guide to training physics-informed neural networks. ArXiv Preprint ArXiv:2308.08468.
19. Perdikaris, P. G., Pappas, G. J., Seidman, J. H., & Kissas, G. (2023). Computer systems and methods for learning operators.
20. Fang, Z., Wang, S., & Perdikaris, P. (2023). Ensemble learning for physics informed neural networks: A gradient boosting approach. ArXiv Preprint ArXiv:2302.13143.
21. Wang, S., & Perdikaris, P. (2023). Long-time integration of parametric evolution equations with physics-informed deeponets. Journal of Computational Physics.
22. Lippe, P., Veeling, B. S., Perdikaris, P., Turner, R. E., & Brandstetter, J. (2023). Modeling accurate long rollouts with temporal neural PDE solvers.
23. Mao, S., Dong, R., Lu, L., Yi, K. M., Wang, S., & Perdikaris, P. (2023). Ppdonet: Deep operator networks for fast prediction of steady-state solutions in disk–planet systems. The Astrophysical Journal Letters.
24. Bhouri, M. A., Joly, M., Yu, R., Sarkar, S., & Perdikaris, P. (2023). Scalable Bayesian optimization with randomized prior networks. Computer Methods in Applied Mechanics and Engineering.
25. Bhouri, M. A., Joly, M., Yu, R., Sarkar, S., & Perdikaris, P. (2023). Scalable bayesian optimization with high-dimensional outputs using randomized prior networks. ArXiv Preprint ArXiv:2302.07260.
26. Kaltenbach, S., Perdikaris, P., & Koutsourelakis, P.-S. (2023). Semi-supervised invertible neural operators for Bayesian inverse problems. Computational Mechanics.
27. Seidman, J. H., Kissas, G., Pappas, G. J., & Perdikaris, P. (2023). Variational autoencoding neural operators. ArXiv Preprint ArXiv:2302.10351.
28. Wang, S., & Perdikaris, P. (2022). Adaptive Training Strategies for Physics-Informed Neural Networks.
29. Gander, L., Pezzuto, S., Gharaviri, A., Krause, R., Perdikaris, P., & Costabal, F. S. (2022). Fast characterization of inducible regions of atrial fibrillation models with multi-fidelity Gaussian process classification. Frontiers in Physiology.
30. Kissas, G., Hwuang, E., Thompson, E. W., Schwartz, N., Detre, J. A., Witschey, W. R., & Perdikaris, P. (2022). Feasibility of Vascular Parameter Estimation for Assessing Hypertensive Pregnancy Disorders. Journal of Biomechanical Engineering.
31. Beckers, T., Seidman, J., Perdikaris, P., & Pappas, G. J. (2022). Gaussian process port-Hamiltonian systems: Bayesian learning with physics prior.
32. Bhouri, M. A., & Perdikaris, P. (2022). Gaussian processes meet NeuralODEs: a Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy data. Philosophical Transactions of the Royal Society A.
33. Wang, S., Wang, H., & Perdikaris, P. (2022). Improved architectures and training algorithms for deep operator networks. Journal of Scientific Computing.
34. Pezzuto, S., Perdikaris, P., & Costabal, F. S. (2022). Learning cardiac activation maps from 12-lead ECG with multi-fidelity Bayesian optimization on manifolds. IFAC-PapersOnLine.
35. Kissas, G., Seidman, J. H., Guilhoto, L. F., Preciado, V. M., Pappas, G. J., & Perdikaris, P. (2022). Learning operators with coupled attention. Journal of Machine Learning Research.
36. Daw, A., Bu, J., Wang, S., Perdikaris, P., & Karpatne, A. (2022). Mitigating propagation failures in physics-informed neural networks using retain-resample-release (r3) sampling. ArXiv Preprint ArXiv:2207.02338.
37. Daw, A., Bu, J., Wang, S., Perdikaris, P., & Karpatne, A. (2022). Mitigating propagation failures in pinns using evolutionary sampling.
38. Tipireddy, R., Perdikaris, P., Stinis, P., & Tartakovsky, A. M. (2022). Multistep and continuous physics-informed neural network methods for learning governing equations and constitutive relations. Journal of Machine Learning for Modeling and Computing.
39. Seidman, J., Kissas, G., Perdikaris, P., & Pappas, G. J. (2022). NOMAD: Nonlinear manifold decoders for operator learning. Advances in Neural Information Processing Systems.
40. Sankaran, S., Wang, H., Guilhoto, L. F., & Perdikaris, P. (2022). On the impact of larger batch size in the training of physics informed neural networks.
41. Yang, Y., Blanchard, A., Sapsis, T., & Perdikaris, P. (2022). Output-weighted sampling for multi-armed bandits with extreme payoffs. Proceedings of the Royal Society A.
42. Herrera, C. R., Grandits, T., Plank, G., Perdikaris, P., Costabal, F. S., & Pezzuto, S. (2022). Physics-informed neural networks to learn cardiac fiber orientation from multiple electroanatomical maps. Engineering with Computers.
43. Wang, S., Wang, H., Seidman, J. H., & Perdikaris, P. (2022). Random weight factorization improves the training of continuous neural representations. ArXiv Preprint ArXiv:2210.01274.
44. Daw, A., Bu, J., Wang, S., Perdikaris, P., & Karpatne, A. (2022). Rethinking the importance of sampling in physics-informed neural networks. ArXiv Preprint ArXiv:2207.02338.
45. Yang, Y., Kissas, G., & Perdikaris, P. (2022). Scalable uncertainty quantification for deep operator networks using randomized priors. Computer Methods in Applied Mechanics and Engineering.
46. Kaltenbach, S., Perdikaris, P., & Koutsourelakis, P.-S. (2022). Semi-supervised invertible deeponets for bayesian inverse problems. Stat.
47. Rao, R., Bolintineanu, D., Ortiz, W., Sankaran, S., Perdikaris, P., Hartt, W., Lindberg, S., & Hamersky, M. (2022). Viscoelastic Free Surface Flows: From Models to Experiments and Somewhere in Between.
48. Wang, S., Yu, X., & Perdikaris, P. (2022). When and why PINNs fail to train: A neural tangent kernel perspective. Journal of Computational Physics.
49. Ji, S., Pang, G., Zhang, J., Yang, Y., & Perdikaris, P. (2021). Accurate artificial boundary conditions for semi-discretized one-dimensional peridynamics. Proceedings of the Royal Society A.
50. Ma, N., Chen, L., Hu, J., Perdikaris, P., & Braham, W. W. (2021). Adaptive behavior and different thermal experiences of real people: A Bayesian neural network approach to thermal preference prediction and classification. Building and Environment.
51. Bhouri, M. A., Costabal, F. S., Wang, H., Linka, K., Peirlinck, M., Kuhl, E., & Perdikaris, P. (2021). COVID-19 dynamics across the US: A deep learning study of human mobility and social behavior. Computer Methods in Applied Mechanics and Engineering.
52. Wang, S., & Perdikaris, P. (2021). Deep learning of free boundary and Stefan problems. Journal of Computational Physics.
53. Wang, H., Crawford-Eng, I., & Perdikaris, P. (2021). Enhancing the trainability and expressivity of deep MLPs with globally orthogonal initialization.
54. Wang, S., Bhouri, M. A., & Perdikaris, P. (2021). Fast PDE-constrained optimization via self-supervised operator learning. ArXiv Preprint ArXiv:2110.13297.
55. Kissas, G., Hwuang, E., Thompson, E. W., Schwartz, N., Detre, J. A., Witschey, W. R., & Perdikaris, P. (2021). Feasibility of vascular remodeling parameter estimation for assessing hypertensive pregnancy disorders. BioRxiv.
56. Wang, S., Wang, H., & Perdikaris, P. (2021). LEARNING THE SOLUTION OPERATOR OF PARAMETRIC PARTIAL DIFFERENTIAL EQUATIONS WITH PHYSICS-INFORMED. ArXiv Preprint ArXiv:2103.10974.
57. Grandits, T., Pezzuto, S., Costabal, F. S., Perdikaris, P., Pock, T., Plank, G., & Krause, R. (2021). Learning atrial fiber orientations and conductivity tensors from intracardiac maps using physics-informed neural networks.
58. Wang, S., Wang, H., & Perdikaris, P. (2021). Learning the solution operator of parametric partial differential equations with physics-informed DeepONets. Science Advances.
59. Reyes, B., Howard, A. A., Perdikaris, P., & Tartakovsky, A. M. (2021). Learning unknown physics of non-Newtonian fluids. Physical Review Fluids.
60. Peng, G. C. Y., Alber, M., Tepole, A. B., Cannon, W. R., De, S., Dura-Bernal, S., Garikipati, K., Karniadakis, G., Lytton, W. W., Perdikaris, P., Petzold, L., & Kuhl, E. (2021). Multiscale modeling meets machine learning: What can we learn?
61. Wang, S., Wang, H., & Perdikaris, P. (2021). On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering.
62. Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2021). Physics informed learning machine.
63. Yu, R., Perdikaris, P., & Karpatne, A. (2021). Physics-guided ai for large-scale spatiotemporal data.
64. Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., & Yang, L. (2021). Physics-informed machine learning.
65. Cai, S., Wang, Z., Wang, S., Perdikaris, P., & Karniadakis, G. E. (2021). Physics-informed neural networks for heat transfer problems.
66. Wang, S., Teng, Y., & Perdikaris, P. (2021). Understanding and mitigating gradient flow pathologies in physics-informed neural networks. SIAM Journal on Scientific Computing.
67. Yang, Y., Bhouri, M. A., & Perdikaris, P. (2020). Bayesian differential programming for robust systems identification under uncertainty. Proceedings of the Royal Society A.
68. Lee, Y. K., Li, X., Perdikaris, P., Crocker, J. C., Reina, C., & Sinno, T. (2020). Hydrodynamic and frictional modulation of deformations in switchable colloidal crystallites. Proceedings of the National Academy of Sciences.
69. Kissas, G., Yang, Y., Hwuang, E., Witschey, W. R., Detre, J. A., & Perdikaris, P. (2020). Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks. Computer Methods in Applied Mechanics and Engineering.
70. Bonfiglio, L., Perdikaris, P., & Brizzolara, S. (2020). Multi-fidelity Bayesian optimization of SWATH hull forms. Journal of Ship Research.
71. Costabal, F. S., Yang, Y., Perdikaris, P., Hurtado, D. E., & Kuhl, E. (2020). Physics-informed neural networks for cardiac activation mapping. Frontiers in Physics.
72. Agrawal, A., Amin, S., Atanasov, N., Banaszuk, A., Bartlett, P., Bayen, A., Boedecker, J., Borrelli, F., Chaudhari, P., Chiuso, A., Coogan, S., Cairano, S. D., Fazel, M., Foster, D., Gharesifard, B., Ghosh, S., Gibson, T., Gil, S., Gu, S., … Wu, C. (2020). The Second Annual Conference on Learning for Dynamics and Control. Proceedings of Machine Learning Research.
73. Tipireddy, R., Perdikaris, P., Stinis, P., & Tartakovsky, A. (2019). A comparative study of physics-informed neural network models for learning unknown dynamics and constitutive relations. ArXiv Preprint ArXiv:1904.04058.
74. Yang, Y., & Perdikaris, P. (2019). Adversarial uncertainty quantification in physics-informed neural networks. Journal of Computational Physics.
75. Yang, Y., & Perdikaris, P. (2019). Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems. Computational Mechanics.
76. Tepole, A. B., Cannon, W., De, S., Dura-Bernal, S., Garikipati, K., Karniadakis, G., Lytton, W., Perdikaris, P., Kuhl, E., Petzold, L., & Alber, M. (2019). Integrating machine learning and multiscale modeling-perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences.
77. Alber, M., Tepole, A. B., Cannon, W. R., De, S., Dura-Bernal, S., Garikipati, K., Karniadakis, G., Lytton, W. W., Perdikaris, P., Petzold, L., & Kuhl, E. (2019). Integrating machine learning and multiscale modeling—perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences.
78. Costabal, F. S., Matsuno, K., Yao, J., Perdikaris, P., & Kuhl, E. (2019). Machine learning in drug development: Characterizing the effect of 30 drugs on the QT interval using Gaussian process regression, sensitivity analysis, and uncertainty quantification. Computer Methods in Applied Mechanics and Engineering.
79. Gulian, M., Raissi, M., Perdikaris, P., & Karniadakis, G. (2019). Machine learning of space-fractional differential equations. SIAM Journal on Scientific Computing.
80. Costabal, F. S., Perdikaris, P., Kuhl, E., & Hurtado, D. E. (2019). Multi-fidelity classification using Gaussian processes: accelerating the prediction of large-scale computational models. Computer Methods in Applied Mechanics and Engineering.
81. Sarkar, S., Joly, M., & Perdikaris, P. (2019). Multi-fidelity learning with heterogeneous domains.
82. Sarkar, S., Mondal, S., Joly, M., Lynch, M. E., Bopardikar, S. D., Acharya, R., & Perdikaris, P. (2019). Multifidelity and multiscale Bayesian framework for high-dimensional engineering design and calibration. Journal of Mechanical Design.
83. Yang, Y., & Perdikaris, P. (2019). Physics-Informed Deep Generative Models for Scalable Uncertainty Quantification.
84. Zhu, Y., Zabaras, N., Koutsourelakis, P.-S., & Perdikaris, P. (2019). Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data. Journal of Computational Physics.
85. Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics.
86. Bonfiglio, L., Perdikaris, P., del Águila, J., & Karniadakis, G. E. (2018). A probabilistic framework for multidisciplinary design: Application to the hydrostructural optimization of supercavitating hydrofoils. International Journal for Numerical Methods in Engineering.
87. Klinghoffer, T., Perez, C. R., Vincent, R., Perdikaris, P., & Chryssostomidis, C. (2018). Applying Image Recognition to Enhance Fisheries Management Capabilities. 98th American Meteorological Society Annual Meeting.
88. Bonfiglio, L., Perdikaris, P., Vernengo, G., Medeiros, J. S. D., & Karniadakis, G. (2018). Improving swath seakeeping performance using multi-fidelity Gaussian process and Bayesian optimization. Journal of Ship Research.
89. Tartakovsky, A. M., Marrero, C. O., Perdikaris, P., Tartakovsky, G. D., & Barajas-Solano, D. (2018). Learning parameters and constitutive relationships with physics informed deep neural networks. ArXiv Preprint ArXiv:1808.03398.
90. Hsieh, M.-ying A., Li, W., Kularatne, D., Zhang, X., Perdikaris, P., & Ke, B. (2018). Machine Learning for Identifying Lagrangian Coherent Structures in Geophysical Flows. AGU Fall Meeting 2018.
91. Kularatne, D., Hsieh, M. Y. A., Li, W., Zhang, X., Perdikaris, P., & Ke, B. (2018). Machine Learning for Identifying Lagrangian Coherent Structures in Geophysical Flows. AGU Fall Meeting Abstracts.
92. Bonfiglio, L., Perdikaris, P., Brizzolara, S., & Karniadakis, G. E. (2018). Multi-fidelity optimization of super-cavitating hydrofoils. Computer Methods in Applied Mechanics and Engineering.
93. Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2018). Multistep neural networks for data-driven discovery of nonlinear dynamical systems. ArXiv Preprint ArXiv:1801.01236.
94. Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2018). Numerical Gaussian processes for time-dependent and nonlinear partial differential equations. SIAM Journal on Scientific Computing.
95. Tartakovsky, G., Tartakovsky, A. M., & Perdikaris, P. (2018). Physics informed deep neural networks for learning parameters with non-Gaussian non-stationary statistics. AGU Fall Meeting Abstracts.
96. Yang, Y., & Perdikaris, P. (2018). Physics-informed deep generative models. ArXiv Preprint ArXiv:1812.03511.
97. Perez, C. R., Klinghoffer, T., Vincent, R., Perdikaris, P., Consi, T., & Chryssostomidis, C. (2018). Withdrawn: Bioelectric Field Measurements: Augmenting Image Recognition for Fisheries Management. 98th American Meteorological Society Annual Meeting.

Patents

1. Perdikaris, P. G., Pappas, G. J., Seidman, J. H., & Kissas, G. (2023). Computer systems and methods for learning operators.
2. Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2021). Physics informed learning machine. Google Patents.