@article{vemuri2026scalable,
    type = {article},
    key = {vemuri2026scalable},
    author = {Sai Karthikeya Vemuri and Tim Büchner and Julia Niebling and Joachim Denzler},
    title = {Scalable and Expressive Physics-Informed Neural Networks via Functional Tensor Decomposition},
    journal = {Pattern Recognition Letters},
    year = {2026},
    issn = {0167-8655},
    doi = {https://doi.org/10.1016/j.patrec.2026.06.027},
    url = {https://www.sciencedirect.com/science/article/pii/S0167865526002291},
    abstract = {Physics-Informed Neural Networks (PINNs) offer a promising framework for solving partial differential equations (PDEs) by embedding physical laws into neural network training. In our prior work, we introduced Functional Tensor Decomposition PINNs (FTD-PINNs), which leverage tensor decomposition to improve the scalability and efficiency of PINNs, especially for high-dimensional PDEs. This work extends our previous study on Functional Tensor Decomposition PINNs by systematically examining how decomposition structure and backend activations affect performance, efficiency, and stability across representative partial differential equations. Using Helmholtz and Klein-Gordon systems as benchmarks, we compare three decomposition modes (CP, Tucker, Tensor-Train) combined with four activation backends (Tanh, Tanh + PE, SIREN, and WIRE). Multi-seed and compute-aware evaluations reveal consistent accuracy-efficiency trade-offs: Tensor-Train provides the most balanced decomposition, while frequency-aware backends such as WIRE and SIREN improve convergence for oscillatory regimes. Pareto analyses across rank and collocation density highlight a clear inflection point of diminishing returns and show that backend choice shifts the optimal configuration across PDE types. Together, these results extend the original FTD-PINN framework with a broader empirical foundation and provide practical guidance for selecting decomposition ranks, collocation densities, and backend activations for efficient PINN design.},
    code = {https://github.com/cvjena/TensorDecompositions4PINNs},
    note = {},
}