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..
Learning Stochastic Multiscale Models
Authors: Andrew F. Ilersich, Prasanth Nair
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We present detailed numerical studies to demonstrate that our learned multiscale models achieve superior predictive accuracy compared to under-resolved direct numerical simulation and closure-type models at equivalent resolution, as well as reduced-order modeling approaches. |
| Researcher Affiliation | Academia | Andrew F. Ilersich Institute for Aerospace Studies University of Toronto Toronto, ON M3H 5T6 EMAIL Prasanth B. Nair Institute for Aerospace Studies University of Toronto Toronto, ON M3H 5T6 EMAIL |
| Pseudocode | No | The paper describes the methodology and components (encoder, SDE, decoder) in detail with mathematical equations and diagrams (e.g., Figure 1 and Figure 2), but it does not present any explicitly labeled 'Pseudocode' or 'Algorithm' blocks or figures. |
| Open Source Code | Yes | Code for reproducing our results is available: https://github.com/ailersic/multiscale-visde. |
| Open Datasets | Yes | Our final test case models a radial dam break using the shallow water equations, from the PDEBench dataset [39]. The data for this test case is a simulation of a 2D Von Kármán vortex street at a Reynolds number of Re = 160 from Günther et al. [38]. |
| Dataset Splits | Yes | The training dataset comprises 20 trajectories, with 5 each for validation and testing. For our multiscale models, we use a coarse macroscale mesh with only nζ = 20 points. We partitioned this trajectory temporally for training, validation, and testing, using the intervals [0, 13], (13, 14], and (14, 15], respectively. We use 900 trajectories for training, 50 trajectories for validation, and 50 trajectories for testing. |
| Hardware Specification | Yes | All experiments were conducted on a system with 24 CPU cores, 128GB RAM, and an NVIDIA RTX4090 GPU. |
| Software Dependencies | No | The paper mentions software tools like Py SINDy [47], Py DMD [48], FEni CS [7], and Gerris flow solver [50], but does not provide specific version numbers for these or other libraries (e.g., Python, PyTorch) used in their implementation. |
| Experiment Setup | Yes | Each model is trained with the Adam optimizer and the loss function is the negative of the ELBO defined in (8). The batch size is 64. The advecting wave models were trained for 50 epochs, Kd V for 100 epochs, Burgers for 100 epochs, cylinder flow for 1000 epochs, and shallow water for 20 epochs. We begin by training an implicit-scale model with an initial learning rate of 10 3. We apply an exponential scheduler that decays the learning rate by 10% every 2000 optimization steps. ... The multiscale model is then trained with a reduced initial learning rate of 10 4 |