# TWIG: A Time-Causal Wavelet Operator for Autoregressive Forecasting on Irregular Graphs

arXiv: https://arxiv.org/abs/2609.22585 · HTML: https://mlsanity.com/paper/2609.22585/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 46 references that are in the map.
- First posted on arXiv 18 Sep 2026.

## Builds on (most cited first, 30 of 30)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [On the Bottleneck of Graph Neural Networks and its Practical Implications](https://mlsanity.com/paper/2006.05205/) (2020)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Rethinking Graph Transformers with Spectral Attention](https://mlsanity.com/paper/2106.03893/) (2021)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [Long Range Graph Benchmark](https://mlsanity.com/paper/2206.08164/) (2022)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [APEBench: A Benchmark for Autoregressive Neural Emulators of PDEs](https://mlsanity.com/paper/2411.00180/) (2024)
- [A deep-learning-based surrogate model for data assimilation in dynamic subsurface flow problems](https://mlsanity.com/paper/1908.05823/) (2019)
- [Towards Stability of Autoregressive Neural Operators](https://mlsanity.com/paper/2306.10619/) (2023)
- [Efficient Learning of Mesh-Based Physical Simulation with BSMS-GNN](https://mlsanity.com/paper/2210.02573/) (2022)
- [Learning Large-scale Subsurface Simulations with a Hybrid Graph Network Simulator](https://mlsanity.com/paper/2206.07680/) (2022)
- [Learning from Predictions: Fusing Training and Autoregressive Inference for Long-Term Spatiotemporal Forecasts](https://mlsanity.com/paper/2302.11101/) (2023)
- [Synthetic Datasets for Machine Learning on Spatio-Temporal Graphs using PDEs](https://mlsanity.com/paper/2502.04140/) (2025)
- [GeoFUSE: A High-Efficiency Surrogate Model for Seawater Intrusion Prediction and Uncertainty Reduction](https://mlsanity.com/paper/2410.20118/) (2024)
- [Variational Encoder-Decoders for Learning Latent Representations of Physical Systems](https://mlsanity.com/paper/2412.05175/) (2024)
- [Time-causal and time-recursive wavelets](https://mlsanity.com/paper/2510.05834/) (2025)

## Abstract (arXiv)

We introduce TWIG (Time-Causal Wavelet Operator for Irregular Graphs), a graph-native neural operator for autoregressive surrogate modeling on static irregular graphs. TWIG transforms each node history into causal multiscale temporal features that separate recent variation from progressively slower memory components, then propagates these features through graph-wavelet operator blocks with gated pointwise channel mixing. The architecture is causal by construction and designed for closed-loop forecasting, where predictions are recursively reused as future inputs. We evaluate TWIG on three irregular-domain forecasting problems spanning regional diffusion, three-dimensional subsurface hydrology, and aerodynamic flow, with graphs ranging from 400 to 5,233 nodes and model capacities from approximately 70k to 10M parameters. TWIG achieves the lowest aggregate rollout errors on the subsurface-hydrology and regional-diffusion benchmarks and ranks second on the 10M-parameter aerodynamic-flow benchmark, behind the GPS Transformer. Across all three settings, TWIG consistently outperforms the corresponding non-time-causal Graph WNO baseline. These results demonstrate that TWIG provides an effective and scalable approach to stable autoregressive forecasting of dynamical fields on irregular graphs.