Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Neuro-Spectral Architectures for Causal Physics-Informed Networks
Authors: Arthur Bizzi, Leonardo Moreira, Márcio Marques, Leonardo Mendonça, Christian de Oliveira, Vitor Balestro, Lucas dos Santos Fernandez, Daniel Yukimura, Pavel Petrov, João Pereira, Tiago Novello, Lucas Nissenbaum
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We validate Neu SA on canonical benchmarks for linear and nonlinear wave equations, demonstrating strong performance as compared to other architectures, with faster convergence, improved temporal consistency and superior predictive accuracy. Code and pretrained models are available in https://github.com/arthur-bizzi/neusa. 3 Experiments We evaluate Neu SA on boundary and initial value problems for three PDEs: the 2D wave equation, the 2D Burgers equation, and the 1D nonlinear sine Gordon equation. In all cases, we address the forward (direct) problem, where the models are trained to learn approximate solutions given known conditions. We compare the performance and accuracy of Neu SA against several established MLP-based PINN architectures: the original PINN [1], QRes [22], FLS [23], and PINNs Former [4]. |
| Researcher Affiliation | Academia | Arthur Bizzi1 , Leonardo Moreira3, Márcio Marques2, Leonardo Mendonça2, Christian Oliveira2, Vitor Balestro2, Lucas Fernandez4, Daniel Yukimura2, Pavel Petrov2, João M. Pereira5, Tiago Novello2, Lucas Nissenbaum2 1École Polytechnique Fédérale de Lausanne (EPFL), 2Instituto de Matemática Pura e Aplicada (IMPA), 3Universidade do Estado do Rio de Janeiro (UERJ), 4Laboratório Nacional de Computação Científica (LNCC), 5University of Georgia (UGA) |
| Pseudocode | Yes | Algorithm 1 Implementation of dimension-wise layers for a two dimensional input |
| Open Source Code | Yes | Code and pretrained models are available in https://github.com/arthur-bizzi/neusa. |
| Open Datasets | Yes | We validate Neu SA on canonical benchmarks for linear and nonlinear wave equations, demonstrating strong performance as compared to other architectures, with faster convergence, improved temporal consistency and superior predictive accuracy. ...The Marmousi reservoir model [63] is a canonical benchmark with highly complex stratified medium in two dimensions... |
| Dataset Splits | No | All models were trained on the interval [0, 1] and then evaluated on the extended interval [0, 2]. We analyzed performance in successive time instants, quantifying how prediction accuracy degrades as the time gets further from the training region. For PINN, QRes, and FLS models, we sample 10, 000 points for the PDE residual, 1000 points for the initial condition and 500 points for the boundary condition. |
| Hardware Specification | Yes | Experiments were executed on an Nvidia RTX 4090 GPU (24 GB VRAM). ...All experiments were executed on identical machines, containing an Nvidia RTX 4090 GPU with 24GB VRAM, an Intel i9-13900K processor, and 128GB RAM. |
| Software Dependencies | Yes | The code is implemented in Python using the libraries Py Torch (version 2.1.0) and torchdyn (version 1.0.6), distributed under the BSD 3-Clause and Apache licenses, respectively. |
| Experiment Setup | Yes | Training setup. Neu SA and all baseline models are implemented in Py Torch [53]. The baseline configurations follow the setups described in PINNs Former [4] and Ro PINN [3]. PINN, QRes, and FLS are initialized using Xavier initialization [54], with the hyperbolic tangent as the activation function (except for the first FLS layer, which acts as a Fourier feature mapping [55, 26]). All remaining hyperparameters were tuned to achieve the best performance for each model (e.g. weights for the initial and boundary condition losses). For the NODEs used in Neu SA, we adopt the implementation given by the Torch Dyn library [56]. The vector fields Fθ are modeled as MLPs with dimensionwise layers (see Appendix B.2) with two hidden layers, Re LU activations, and Glorot initialization, and are integrated using a fourth-order Runge Kutta solver. Gradients are computed via standard backpropagation through the ODE solver. Training is performed using the Adam optimizer [57]. Neu SA s strong architectural priors enable the use of larger learning rates compared to the baseline models, which are trained with the recommended rate of 10 3 (see 6.1 of [58]). |