Amanda Howard

Amanda Howard

Mathematician

Scientific machine learning

We are interested in machine learning methods for scientific data. Our methods are designed to exploit knowledge about the system to provide more accurate predictions from science, including physics-informed machine learning, multifidelity machine learning, and increased interpretability with Kolmogorov-Arnold networks.

Kolmogorov-Arnold Networks

Standard multilayer perceptrons have fixed activation functions with trainable weights and biases. Kolmogorov-Arnold networks (KANs) use trainable activation functions. This change increases interpretability of the trained network, allowing for learning governing laws directly.

Relevant publications

  1. Howard, Amanda A., Zolman, Nicholas, Jacob, Bruno, Brunton, Steven L., & Stinis, Panos (2026). SINDy-KANs: Sparse identification of non-linear dynamics through Kolmogorov-Arnold networks. arXiv:2603.18548.

  2. Jacob, Bruno, Howard, Amanda A., & Stinis, Panos (2025). Bridging quantum and classical computing for partial differential equations through multifidelity machine learning. arXiv:2512.05241.

  3. Jacob, Bruno, Howard, Amanda A., & Stinis, Panos. (2025). SPIKANs: Separable Physics-Informed Kolmogorov-Arnold Networks. Machine Learning: Science and Technology, 6.3, 035060.

  4. Howard, Amanda A., Jacob, Bruno, & Stinis, Panos. (2025). Multifidelity Kolmogorov-Arnold networks. Machine Learning: Science and Technology, 6.3, 035038.

  5. Howard, Amanda A., Jacob, B., Murphy, S. H., Heinlein, A., & Stinis, P. (2024). Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems. arXiv:2406.19662.

Multifidelity machine learning

In multifidelity machine learning, we train using two or more datasets simultaneously. The low fidelity data is less expensive to produce, but contains less information about the system. The high fidelity data contains more information, but is more expensive. Our goal is to use both datasets to learn a model that is more accurate than either on its own. We have developed Multifidelity Deep Operator Networks and used multifidelity training to improve training of PINNs and continual learning.

Relevant publications

  1. Howard, Amanda A., Jacob, Bruno, & Stinis, Panos. (2025). Multifidelity Kolmogorov-Arnold networks. Machine Learning: Science and Technology, 6.3, 035038.

  2. Heinlein, Alexander, Howard, Amanda A., Beecroft, Damien, & Stinis, Panos. (2025). Multifidelity domain decomposition-based physics-informed neural networks for time-dependent problems. De Gruyter Proceedings in Mathematics.

  3. Howard, Amanda A., Fu, Yucheng, & Stinis, Panos. (2024). A multifidelity approach to continual learning for physical systems. Machine Learning: Science and Technology 5.2, 025042.

  4. Howard, Amanda A., Perego, Mauro, Karniadakis, George E., & Stinis, Panos. (2023). Multifidelity deep operator networks for data-driven and physics-informed problems. Journal of Computational Physics, 493, 112462.

  5. Howard, Amanda A., Yu, Tong, Wang, Wei, & Tartakovsky, Alexandre M. (2022). Physics- informed CoKriging model of a redox flow battery. Journal of Power Sources 542, 231668.

Physics-informed machine learning

In physics-informed machine learning, we use physics, instead of data, to train a neural network. We have developed methods for improved physics-informed training with adaptive weighting methods.

Relevant publications

  1. Chen, Wenqian, Howard, Amanda A., & Stinis, Panos (2026). Self-adaptive weighting and sampling for physics-informed neural networks. Machine Learning: Science and Technology, 7, 025050.

  2. Williams, Emily, Howard, Amanda A., Qadeer, Saad, Meuris, Brek, & Stinis, Panos. (2026). What do physics-informed DeepONets learn? Understanding and improving training for scientific computing applications. Journal of Computational Physics, 558, 114851.

  3. Chen, Wenqian, Howard, Amanda A., & Stinis, Panos (2025). Self-adaptive weights based on balanced residual decay rate for physics-informed neural networks and deep operator networks. Journal of Computational Physics, 542, 114226.

  4. Howard, Amanda A., Yu, Tong, Wang, Wei, & Tartakovsky, Alexandre M. (2022). Physics- informed CoKriging model of a redox flow battery. Journal of Power Sources 542, 231668.
  5. Reyes, Brandon, Howard, Amanda A., Perdikaris, Paris, & Tartakovsky, Alexandre M. (2021). Learning unknown physics of non-Newtonian fluids. Phys. Rev. Fluids, 6, 073301.