GridSFM: A Foundation Model for Solving AC Optimal Power Flow
27d
- Published
- Collected
Authors
Luke Bhan, Weiwei Yang, Margaret Capetz, Baosen Zhang
Categories
We introduce GridSFM, a framework that combines a pretrained foundation model across grid topologies with physics-informed fine-tuning for solving AC Optimal Power Flow (AC-OPF) at scale. It is a 15 million parameter physics-inspired graph neural network pretrained across 54 topologies of 500 to 4{,}000 buses. Our model attains a 2.45\% zero-shot generation-cost error on a 10{,}000 bus case held-out operating conditions with no degradation as system size grows. Building on this, we pair the pretrained backbone with a physics-informed fine-tuning design based on Newton's method for power flow. With only 100 solved instances, GridSFM adapts to unseen grids up to 10{,}000 buses. We show it out performs single topology, dedicated neural network models that are trained more data, both in terms of cost and solver iterations when deployed as warm starting points. In designing this foundation model, we overcome the fact that the feasible set for AC-OPF can be disconnected. This is an obstruction that prevents any continuous neural network from approximating the solution map. To do so, we lift the problem and relax its constraints with logarithmically penalized slacks. We prove that the resulting elastic feasible set is contractible, that the AC-OPF minimizers remain minimizers of the elastic problem above an explicit penalty threshold, and that projecting an approximate solution back onto the AC-OPF feasible set is well posed. We release all models, data, and code so that the community can build on a shared starting point for AC-OPF.
overfeed.news indexes and links. We publish a short excerpt — the full article stays at arXiv AI Papers.
More from arXiv AI Papers
Log in to follow this source
LongZero: Enhancing Long-Context Reasoning in LLMs from Zero Data
Reinforcement learning (RL) is an effective way to strengthen the long-context reasoning of large language models (LLMs), but it needs training data that are long, diverse, challenging, and verifiable. Human annotation of such data is expensive, naturally occurring data are too scarce to sustain RL, and existing synthesis methods depend on external corpora or stronger teacher models, which become harder to obtain as the trained models get stronger. Recently, RL from zero data, in which a model learns from tasks it proposes itself, has achieved excellent performance, but existing methods target short-context tasks. Therefore, we propose LongZero, a method that lets an LLM improve its own long-context reasoning without any external data. Instead of writing questions and answers over existing documents, LongZero first has the model synthesize the question and answer with its supporting evidence in a compact structured form, and only then separately expands the evidence into a long multi-document context. LongZero combines these self-written multi-hop reasoning tasks with self-written multi-round retrieval tasks and trains the model with GRPO. We evaluate LongZero on two LLMs across five long-context reasoning benchmarks and compare it with RL on data synthesized from external corpora. Experimental results show that LongZero can generalize to real tasks, and outperforms both baselines, suggesting a viable and promising path to improving long-context reasoning of LLMs.
Think Harder Where It Matters: Item-Level Adaptive Recursion for Sequential Recommendation
Existing sequential recommenders usually allocate a fixed computational budget to every item in a user's interaction history, regardless of the item's contribution to the final prediction. We challenge this de facto design with two diagnostic findings. (1) Non-uniform computational need: items within the same sequence vary drastically in how much computation they require. Most converge after shallow processing while a critical minority only stabilizes at full depth. (2) Suboptimality of fixed allocation: given oracle access to the target item, a non-uniform depth assignment consistently outranks the fixed one, indicating that existing uniform computation both wastes capacity on already-converged items and sacrifices overall recommendation quality. These observations motivate a shift from fixed-depth computation to item-level adaptive reasoning. To this end, we propose LoopRec. LoopRec recursively applies a single weight-shared block and introduces a lightweight gate at each recursion boundary that makes a binary exit-or-continue decision for every item independently. Items whose representations have sufficiently matured exit early, while those requiring deeper reasoning continue to subsequent recursions. This design converts the fixed global depth into a learned, per-item property without auxiliary depth labels, and is readily adaptable to diverse backbone architectures. Extensive experiments on public benchmarks with four backbone families demonstrate that LoopRec consistently outperforms matched fixed-depth counterparts. Further analysis reveals that LoopRec's learned allocation exhibits interpretable patterns aligned with our post-hoc oracle analysis: lower-frequency items and more recent interactions naturally receive deeper computation. Our code is available at https://github.com/Elpmis117/LoopRec.
PhysiCalWorld: In-Context Physics Calibration for World Models
Existing world models typically perceive a scene through current visual frame or a narrow history window. However, these observations may not reveal the physics properties that determine transition dynamics, such as an object's mass distribution, joint damping, or surface friction. Without calibrating these physics factors for world models, predictions tend to regress toward an empirical prior and induce severe drift in novel test scenes. To this end, we propose PhysiCalWorld, which calibrates action-conditioned world models to the instance-specific dynamics via in-context prompting, without fine-tuning or analytical physics modeling. Our method encodes an exploratory interaction clip collected within the test scene into a compact physics descriptor token, which grounds subsequent predictions in the scene's actual physical behavior. PhysiCalWorld is trained end-to-end with the latent prediction loss alone, without physics labels. At inference time, the descriptor token is extracted once and can be reused across rollouts with negligible compute overhead. We evaluate PhysiCalWorld across four environments covering diverse physics variations and show that it substantially improves rollout prediction accuracy and visual planning success rate. The learned descriptors also form a physically structured latent space and generalize beyond the physics ranges seen during training.
A Quasipolynomial Algorithm for _Contractions
We give an algorithm for computing an -approximate fixed point of any d-dimensional nonexpansion with respect to the _norm in time (1/)^{O(^2 d)}. At its core, our method uses a boosting argument to geometrically shrink a search region. Among other consequences, our algorithm implies that simple stochastic games can be solved in quasipolynomial time.