Kamaljeet Singh

Siddharth Mansingh, James Amarel, Ragib Arnab et al.

Partial Differential Equations (PDEs) are the bedrock for modern computational sciences and engineering, and inherently computationally expensive. While PDE foundation models have shown much promise for simulating such complex spatio-temporal phenomena, existing models remain constrained by the pretraining datasets and struggle with auto-regressive rollout performance, especially in out-of-distribution (OOD) cases. Furthermore, they have significant compute and training data requirements which hamper their use in many critical applications. Inspired by recent advances in ``thinking" strategies used in large language models (LLMs), we introduce the first test-time computing (TTC) strategy for PDEs that utilizes computational resources during inference to achieve more accurate predictions with fewer training samples and smaller models. We accomplish this with two types of reward models that evaluate predictions of a stochastic based model for spatio-temporal consistency. We demonstrate this method on compressible Euler-equation simulations from the PDEGym benchmark and show that TTC captures improved predictions relative to standard non-adaptive auto-regressive inference. This TTC framework marks a foundational step towards more advanced reasoning algorithms or PDE modeling, inluding building reinforcement-learning-based approaches, potentially transforming computational workflows in physics and engineering.

James Amarel, Nicolas Hengartner, Robyn Miller et al.

Foundation models trained as autoregressive PDE surrogates hold significant promise for accelerating scientific discovery through their capacity to both extrapolate beyond training regimes and efficiently adapt to downstream tasks despite a paucity of examples for fine-tuning. However, reliably achieving genuine generalization - a necessary capability for producing novel scientific insights and robustly performing during deployment - remains a critical challenge. Establishing whether or not these requirements are met demands evaluation metrics capable of clearly distinguishing genuine model generalization from mere memorization. We apply the influence function formalism to systematically characterize how autoregressive PDE surrogates assimilate and propagate information derived from diverse physical scenarios, revealing fundamental limitations of standard models and training routines in addition to providing actionable insights regarding the design of improved surrogates.

Mohammadreza Zolfaghari, Kamaljeet Singh, Thomas Brox

The state of the art in video understanding suffers from two problems: (1) The major part of reasoning is performed locally in the video, therefore, it misses important relationships within actions that span several seconds. (2) While there are local methods with fast per-frame processing, the processing of the whole video is not efficient and hampers fast video retrieval or online classification of long-term activities. In this paper, we introduce a network architecture that takes long-term content into account and enables fast per-video processing at the same time. The architecture is based on merging long-term content already in the network rather than in a post-hoc fusion. Together with a sampling strategy, which exploits that neighboring frames are largely redundant, this yields high-quality action classification and video captioning at up to 230 videos per second, where each video can consist of a few hundred frames. The approach achieves competitive performance across all datasets while being 10x to 80x faster than state-of-the-art methods.