Decoding Partial Differential Equations: Cross-Modal Adaptation of Decoder-only Models to PDEs

Abstract: LLMs have shown great success on natural language tasks in recent years, but they have also shown great promise when adapted to new modalities, e.g., for scientific machine learning tasks. Even though decoder-only models are more popular within NLP and scale exceedingly well at generating natural language, most proposed approaches for cross-modal adaptation focus on encoder-only models, raising the question of how model architecture affects these approaches. In this paper, we therefore perform a series of ablation studies to answer this question, systematically comparing encoder-only and decoder-only models on cross-modal adaptation for time-dependent simulation tasks based on partial differential equations (PDEs). We find that decoder-only models are far worse than encoder-only models, when existing approaches are applied unmodified. In contrast to several other domains, scaling decoder-only models also does not help. To harness the potential of decoder-only models in this context, we introduce two novel approaches, Parallel Flipping and Sequence Doubling, attempting to mimic bidirectionality in autoregressive models. Both our methods improve overall performance using decoder-only models for all tasks and all cross-model adaptation methods, closing the gap to encoder-only model performance. We hope that our findings broaden the spectrum of models used on cross-modal adaptation tasks to further scientific ML.