Publications listed in chronological order.

• Boullé, N., Colbrook, M.J. (2025) “On the Convergence of Hermitian Dynamic Mode Decomposition,” Physica D: Nonlinear Phenomena2, Volume 473, 134405
• Burns, T., Fukai, T., Earls, C.J. (2024) “Associative memory inspires improvements for in-context learning using a novel attention residual stream architecture,” arxiv:2412.15113
• Boullé, N., Herremans, A., Huybrechs, D. (2024) “Multivariate rational approximation of functions with curves of singularities,” SIAM Journal of Scientific Computing, Volume 46, Issue 6
• Padmanabha, G., Fuhg, J., Safta, C., Jones, R., Bouklas, N. (2024) “Improving the performance of Stein variational inference through extreme sparsification of physically-constrained neural network models,” Computer Methods in Applied Mechanics and Engineering, Volume 432, 117359
• Runkel, C., Xiao, S., Boullé, N., Chen, Y. (2024) “Operator learning regularization for macroscopic permeability prediction in dual-scale flow problem,” arxiv:2412.00579
• Goldshlager, G.., Abrahamsen, N., Lin, L. (2024) “A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions,” Journal of Computational Physics, Volume 516, 113351
• Sarfati, R., Liu, T.J.B., Boullé, N., Earls, C.J. (2024) “Lines of Thought in Large Language Models,” arxiv:2410.01545
• Liu, T.J.B., Boullé, N., Sarfati, R., Earls, C.J. (2024) “Density estimation with LLMs: a geometric investigation of in-context learning trajectories,” arxiv:2410.05218
• Lim, S.H., Wang, Y., Yu, A., Hart, E., Mahoney, M.W. ,Li, X.S.,  Erichson, N.B. (2024) “Elucidating the Design Choice of Probability Paths in Flow Matching for Forecasting,” arxiv.org:2410.03229
• Zekri, O., Odonnat, A., Benechehab, A., Bleistein, L., Boullé, N., Redko, I. (2024) “Large Language Models as Markov Chains,” arxiv:2410.02724
• Yu, A., Lyu, D., Lim, S.H., Mahoney, M.W., Erichson, N.B. (2024) “Tuning Frequency Bias of State Space Models,” arxiv:2410.02035
• Eghtesad, A., Tan, J., Fuhg, J., Bouklas, N. (2024) “NN-EVP: A physics informed neural network-based elasto-viscoplastic framework for predictions of grain size-aware flow response,” International Journal of Plasticity, Volume 181, 104072
• Bouziani, N., Boullé, N. (2024) “Structure-Preserving Operator Learning,” arxiv:2410.01065
• Gregory, W., MacEachern, R., Takao, S., Lawrence, I., Nab, C., Deisenroth, M., Tsamados, M. (2024) “Scalable interpolation of satellite altimetry data with probabilistic machine learning,” Nature Communications, 15, 7453
• Van Wees, L. Shankar, K., Fuhg, J., Bouklas, N., Shade, P., Obstalecki, M. Kasemer, M. (2024) “Establishing the relationship between generalized crystallographic texture and macroscopic yield surfaces using partial input convex neural networks,” Materialia, Volume 36, 102151
• Graf, E., Townsend, A. (2024) “Numerical Instability of Algebraic Rootfinding Methods,” arxiv:2408.02805
• Au, C., Tsamados, M., Manescu, P., Takao, S. (2024) “ARISGAN: Extreme super-resolution of arctic surface imagery using generative adversarial networks,” Frontiers in Remote Sensing, Volume 5
• Bunker, J., Girolami, M., Lambley, H., Stuart, A., Sullivan, T.J. (2024) “Autoencoders in Function Space,” arxiv:2408.01362
• Bhattacharya, K., Kovachki, N., Rajan, A., Stuart, A., Trautner, M. (2024) “Learning Homogenization for Elliptic Operators,” SIAM Journal on Numerical Analysis, Volume 62, Issue 4
• Li, K., Ko, H., DiStasio, R., Damle, A. (2024) “Unambiguous and robust formulation for Wannier localization,” American Physical Society, Volume 110, Issue 8, 085127
• Chen, Y., Huang, D., Huang, J., Reich, S., Stuart, A. (2024) “Efficient, Multimodal, and Derivative-Free Bayesian Inference With Fisher-Rao Gradient Flows,” arxiv:2406.17263
• Lu, F., Zlobina, K., Rondoni, N., Teymoori, S Gomez, M. (2024) “Enhancing wound healing through deep reinforcement learning for optimal therapeutics,” Royal Society Open Science, Volume 11, Issue 7, 11240228
• Leung, S.C., Zhou, D., Bae, J. (2024) “Integrated Gradients for Optimal Surface Pressure Sensor Placement for Lift Prediction of an Airfoil Subject to Gust,” AIAA, 4148
• Sit, H., Keith, B., Bergen, K. (2024) “Improving Explainability of Softmax Classifiers Using a Prototype-Based Joint Embedding Method,” https://arxiv.org/abs/2407.02271
• Chen, W., Tsamados, M., Willatt, R., Takao, S., Brockley, D., de Rijke-Thomas, C., Francis, A., Johnson, T., Landy, J., Lawrence, I., Lee, S., Shirazi, D., Liu, W., Nelson, C., Stroeve, J., Hirata, L., Deisenroth, M. (2024) “Co-located OLCI optical imagery and SAR altimetry from Sentinel-3 for enhanced Arctic spring sea ice surface classification,” Frontiers in Remote Sensing, Volume 5
• Ding, Z., Ko, T., Yao, J., Lin, L., Li, X. (2024) “Random coordinate descent: A simple alternative for optimizing parameterized quantum circuits,” Physical Review Research, Volume 6, Issue 3,
• Narayanan, A., Bergen, K. (2024) “Prototype-Based Methods in Explainable AI and Emerging Opportunities in the Geosciences,” https://openreview.net/pdf?id=iFjtwefAjZ
• Li, K., Damle, A. (2024) “Automating Variational Differentiation,” arxiv:2310.0945
• Calvello, E., Kovachki, N., Levine, M., Stuart, A. (2024) “Continuum Attention for Neural Operators,” arxiv:2406.06486
• Anderka, R., Deisenroth, M. Takao, S. (2024) “Iterated INLA for State and Parameter Estimation in Nonlinear Dynamical Systems,” arxiv:2402.17036
• Flynn, M., Wang, A., Alvarez, D.E., De Sa, C., Damle, A. (2024) “STAT: Shrinking Transformers After Training,” arXiv:2406.00061
• Akyildiz, O.D., Girolami, M., Stuart, A, Vadeboncoeur, A. (2024) “Efficient Prior Calibration From Indirect Data,” arXiv:2405.17955v1
• J.-L. Wu, M. E. Levine, T. Schneider, A. Stuart; Learning about structural errors in models of complex dynamical systems; Journal of Computational Physics, 513 (2024) 113157
• Yu, A., Mahoney, M.W., Erichson, B. (2024) “There is HOPE to Avoid HiPPOs for Long-memory State Space Models,” arXiv:2405.13975
• Boullé, N., Colbrook, M.J. (2024) “Multiplicative Dynamic Mode Decomposition,” arXiv:2405.05334
• Fuhg, J., Padmanabha, G., Bouklas, N., Bahmani, B., Sun, W., Vlassis, N., Flaschel, M., Carrara, P., De Lorenzis, L. (2024) “A review on data-driven constitutive laws for solids,” arxiv:2405.03658
• Damle, A., Glas, S., Townsend, A., Yu, A. (2024) “How to reveal the rank of a matrix?,” arXiv:2405.04330
• Lanthaler, S., Stuart, A. Trautner, M. (2024) “Discretization Error of Fourier Neural Operators,” https://arxiv.org/abs/2405.02221
• Key, O., Takao, S., Giles, D., Deisenroth, M. (2024) “Scalable Data Assimilation with Message Passing,” arxiv:2404.12968
• Persson, D., Boullé, N., Kressner, D. (2024) “Randomized Nyström approximation of non-negative self-adjoint operators,” arXiv:2404.00960
• Amsel, N., Chen, T., Keles, F.D., Halikias, D., Musco, C., Musco, C. (2024) “Fixed-sparsity matrix approximation from matrix-vector products,” arXiv:2402.09379
• Carrillo, J.A., Hoffman, F., Stuart, A.M., Vaes, U. (2024) “Statistical Accuracy of Approximate Filtering Methods,” arXiv:2402.01593
• Colbrook, M.J., Li, Q., Raut, R.V. and Townsend, A., (2024) “Beyond expectations: residual dynamic mode decomposition and variance for stochastic dynamical systems,” Nonlinear Dynamics, 112(3), pp.2037-2061.
• Liu, T.J.B., Boullé, N., Sarfati, R., Earls, C.J. (2024) “LLMs learn governing principles of dynamical systems, revealing an in-context neural scaling law,” ICML Workshop on In-Context Learning.
• Boullé, N., Halikias, D., Otto, S.E., Townsend, A. (2024) “Operator learning without the adjoint,” arXiv:2401.17739
• Boullé, N., Townsend, A. (2024) “A Mathematical Guide to Operator Learning,” Handbook of Numerical Analysis, 25, p. 83-125.
• Laakmann, F., Boullé, N. (2024) “Bifurcation analysis of a two-dimensional magnetic Rayleigh-Bénard problem,” Physica D: Nonlinear Phenomena, 467, 134270.
• Wang, C., Townsend, A. (2023) “Operator learning for hyperbolic partial differential equations,” arXiv:2312.17489
• Zvonek, J., Horning, A., Townsend, A. (2023) “ContHutch++: Stochastic trace estimation for implicit integral operators,” arxiv:2311.07035
• Armstrong, R., Buzali, A., and Damle, A. (2023) “Structure-Aware Analyses and Algorithms for Interpolative Decompositions,” https://arxiv.org/abs/2310.0945