Physics-Informed Metacognition: Improving LLMs Self-Knowledge via Physical Constraints

Mahule Roy, Subhas Roy

Keywords: Metacognition, large language models, uncertainty calibration, self-reflection, physics-informed learning, epistemic grounding, change-of-mind behavior, scientific reasoning, self-knowledge, trustworthiness

TL;DR: We introduce Physics-Informed Metacognition (PIM), a framework that teaches LLMs to evaluate and revise their own reasoning using physical laws as objective self-reflection signals.

Abstract: Large language models (LLMs) exhibit remarkable capabilities in scientific reasoning yet struggle with reliable self-assessment and uncertainty quantification—core aspects of metacognition. We introduce Physics-Informed Metacognition (PIM), a novel framework that embeds physical constraints into generative models to enhance their self-knowledge capabilities. PIM integrates physics informed variational autoencoders (PI-VAE) with adapter-based fine-tuning of LLMs, enabling models to leverage physical consistency as an additional signal for metacognitive calibration. We conduct comprehensive evaluations across established physics reasoning benchmarks including PhysiNet, OpenPhys, and symbolic mathematics datasets. Our results demonstrate that PIM significantly improves metacognitive capabilities, including calibration metrics (reducing ECE by 37.2%), selective prediction performance (increasing AUC by 18.6%), and change-of-mind behavior (improving COMS by 42.8%) compared to state-of-the art baselines. The framework provides a principled approach for building more self-aware AI systems in scientific domains that can not only reason but also understand the limits of their knowledge. By grounding confidence in physical consistency, PIM enables both metacognitive monitoring (detecting likely errors) and metacognitive control (revising beliefs based on self-evaluation).

Submission Number: 10