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Decoupled Physical Modeling and Execution for Physics Reasoning

Ye Zhang, Xuehang Guo, Rui Pan, Pengfei Yu, Denghui Zhang, Manling Li, Qingyun Wang

arXiv:2608.22126v1cs.LGcs.CL

TL;DR

Physics reasoning suffers when physical modeling and mathematical execution are conflated. The paper introduces structured modeling traces with SFT and rubric-guided GRPO, and reports consistent improvements across multimodal benchmarks, including stronger gains for weaker models. The approach’s scope and data quality remain constrained by noisy automatically generated traces, unexplored cross-domain generalization, and added judge-based RL compute.

  • Problem

    MLLMs tend to conflate physical modeling with mathematical execution in physics reasoning, leading to conceptual errors despite stronger performance in mathematical and logical reasoning.

  • Method

    The framework introduces structured physical modeling traces as an intermediate representation and trains models with SFT followed by rubric-guided GRPO.

  • Results

    Explicitly improving physical modeling consistently improves reasoning performance across multiple multimodal physics benchmarks.

  • Takeaways & Limitations

    Separating physical modeling from mathematical execution provides an effective strategy for improving physics reasoning in the evaluated models and benchmarks.

  • Takeaways & Limitations

    The method depends on automatically generated traces and physics-specific criteria that remain noisy, has unexplored generalization beyond physics, and adds LLM-as-a-judge compute cost.

Abstract

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Physics reasoning requires constructing a consistent model of the underlying physical system rather than relying solely on symbolic or formula-based manipulation. Although large language models have shown strong ability in solving math and coding problems, they still struggle with physics problems, as these problems entangle the physical modeling process with mathematical calculations. Humans approach physics by first building a representation of the system before performing calculations. Inspired by this, we introduce a unified framework that distills intermediate representations that explicitly encode the physical modeling process and adopt a two-stage post-training strategy, where supervised fine-tuning establishes structured modeling, and reinforcement learning with rubric-based feedback improves the quality of the modeling process. Experiments on multiple multimodal physics benchmarks show that our approach leads to consistent improvements in reasoning performance across different models and datasets. On PhysReason, PhyX and SeePhys benchmarks, physical modeling output performs GRPO by an average ~3%, showing that explicit physical modeling is an efficient strategy of improving physics reasoning for small LLMs.

1 Introduction

Physics reasoning can fail when models conflate physical modeling with mathematical execution. The framework addresses this by explicitly representing physical modeling before execution and reports consistent benchmark improvements.

  • Physics reasoning requires a structured representation of relevant principles and relationships, not symbolic manipulation alone.
  • MLLMs often conflate physical modeling and mathematical execution, producing conceptual errors such as incorrect force-arm identification.The reported error overestimates angular acceleration and final cable speed.
  • The framework represents physics reasoning as physical modeling followed by mathematical execution using structured physical modeling traces.
  • The training framework constructs structured modeling plans and physics-related rubrics before supervised fine-tuning and rubric-based GRPO.
  • Explicitly modeling the physical system consistently improves performance on open-ended multimodal physics reasoning benchmarks.

2 Structured Physical Modeling for Physics Reasoning

The framework separates physical modeling from mathematical execution through an intermediate representation and trains models with structured supervision followed by rubric-guided reinforcement learning. Its data pipeline constructs and verifies modeling trajectories, derives criteria from them, and combines text-only with multimodal training.

  • 2.1 Overview and Task Formulation: Physics problem solving is decomposed into physical modeling and mathematical execution stages.The model generates τ from input problem x, then produces execution and answer outputs (z, y) conditioned on that representation.
  • 2.1 Overview and Task Formulation: The model factorizes reasoning as generating a modeling trace before generating execution and final-answer outputs.
  • 2.1 Overview and Task Formulation: SFT provides a cold start, while rubric-guided GRPO refines modeling quality and encourages physically grounded representations.
  • 2.2 Physics-Modeling Data Construction: Training data combines multimodal pools from PhysReason, PhyX, and SeePhys with text-only pools from SCP-116K and MegaScience.Additional multimodal problems are synthesized while preserving underlying physical principles and concepts.
  • 2.2 Physics-Modeling Data Construction: Verified physical modeling trajectories are used to derive rubrics with visual, modeling, planning, and execution criteria.Each criterion includes a textual specification and adaptive weight reflecting its relative importance.
  • 2.3 Two-Stage Post-Training: The post-training pipeline applies SFT to structured trajectories and uses GRPO rewards combining answer correctness, format validity, and rubric-based modeling evaluation.Text-only data establishes the modeling format before multimodal data teaches visual grounding.

3 Results

Across models and benchmarks, explicitly structured physical modeling improves physics reasoning, with especially clear gains for weaker models and under limited token budgets. Ablations and subfield analyses indicate complementary benefits from SFT and rubric-based GRPO, with larger gains in mechanics and electrodynamics.

  • Performance of Physical Modeling: P@1/P@5 on PhysReason rises from 13.3/33.6 to 22.9/47.1 for Qwen2.5-VL-3B and from 25.0/47.8 to 32.1/58.2 for Qwen2.5-VL-7B.The gains are especially clear for relatively weak base models.
  • Performance of Physical Modeling: Qwen3-VL-8B improves from 51.8/70.7 to 53.3/74.7 on PhysReason and from 43.2/61.4 to 45.1/64.8 on PhyX.The improvement is relatively marginal because the base model already performs strongly.
  • Effect of SFT Cold Start: SFT cold start performs more strongly under smaller token budgets, while the baseline continues improving as its token budget increases.This pattern suggests that physical modeling can make reasoning more concise, whereas the baseline often relies on longer reflective traces.
  • Ablation Studies: Removing either SFT cold start or rubric reward consistently weakens performance, and the full method achieves the best or tied-best performance across all benchmarks.SFT supplies structured-modeling initialization, while rubric-based reinforcement learning encourages more effective use of those structures.
  • Subfield-wise Analysis: Physics-Modeling + GRPO consistently improves performance across most subfields, with the largest gains in mechanics and electrodynamics.Optics and thermodynamics show relatively smaller improvements and involve geometric ray configurations or thermodynamic-state and energy-transfer reasoning.
  • Qualitative Analysis: In a coupled Carnot engine–refrigerator example, structured modeling transfers available work from the engine stage to the refrigerator stage before numerical execution.The intermediate representation organizes variables, constraints, and governing relations for coherent multi-step reasoning.

4 Conclusion

The paper separates physics reasoning into physical modeling and mathematical execution, using an intermediate representation and two-stage post-training. Across multimodal benchmarks, explicitly improving physical modeling produces more reliable reasoning performance.

  • 4 Conclusion: The framework separates physical modeling from mathematical execution and introduces an intermediate representation that explicitly captures the modeling stage.Its training pipeline combines structured supervision, supervised fine-tuning, and rubric-based reinforcement learning.
  • 4 Conclusion: Experiments across multiple multimodal physics benchmarks show that explicitly improving physical modeling leads to more reliable reasoning performance.

Limitations

The method depends on automatically generated modeling traces and physics-specific criteria whose quality remains tied to the underlying models' reasoning ability. Its scope is currently physics reasoning, and rubric-based reinforcement learning adds training compute cost.

  • Limitations: Automatically generated physical-modeling traces and physics-specific criteria can still contain noise and flawed modeling despite multi-stage verification.Their quality depends on the underlying LLMs' reasoning ability.
  • Limitations: The framework is designed for physics reasoning, so its generalization to other domains remains unexplored.
  • Limitations: Rubric-based reinforcement learning introduces additional compute cost because training requires an LLM-as-a-judge.

C.1 Data Source

The data pipeline combines established textual and multimodal physics sources with synthesized problems, then filters and validates structured physical modeling traces. The resulting rubrics encode visual grounding, physical concepts, planning, and execution.

  • Data sources: PhysReason, PhyX, and SeePhys provide multimodal physics problems, while SCP-116K and MegaScience provide textual scientific reasoning data.The multimodal benchmarks emphasize diagram-grounded or visually integrated physics reasoning, whereas the textual sources provide broader STEM problem–solution data.
  • Data augmentation: Problem augmentation varies objectives, numerical values, and wording while preserving the underlying physical setup or semantics.The transformations expand diversity without changing the intended physical principles.
  • Structured modeling: Structured modeling inputs combine the image, question, generated caption, and reference solution, with trajectories required to represent the system explicitly.The representation includes system understanding and constraints, while captions describe observable physical elements and quantities.
  • Quality control: Candidate traces are filtered for internal coherence, multimodal consistency, and modeling specificity before execution-based validation.Only plans that support correct downstream solutions are retained, ensuring both physical grounding and executability.
  • Rubric construction: Rubrics are derived from verified traces and use atomic, verifiable, physically grounded criteria covering visual information, modeling, planning, and execution.This converts modeling traces into explicit supervision for the physical reasoning process.

D Data Statistics

The constructed multimodal physical modeling trajectory dataset contains 8,880 trajectories drawn from original and synthesized samples, with coverage reported across major physics categories.

  • Dataset size: 8,880 physical trajectories constitute the final multimodal physical modeling trajectory dataset.The dataset statistics are summarized by category in Table 4.
  • Dataset composition: 4,852 trajectories are original samples and 4,028 are synthesized samples.The two sources are relatively balanced in the final dataset.
  • Category coverage: The dataset provides relatively balanced coverage across major physics categories.Table 4 reports the category-level statistics of the constructed dataset.

E Two-stage Post-training for Physical Modeling

The post-training framework separates physical modeling from mathematical execution, first teaching structured trajectories with SFT and then refining them with rubric-guided GRPO rewards.

  • Two-stage formulation: Structured reasoning trajectories contain physical modeling τ, execution z, and the final answer y.The model generates τ first and then produces execution and answer outputs based on that representation.
  • SFT cold start: SFT provides a cold start for generating structured reasoning trajectories before reinforcement learning.Training progresses from text-only data to multimodal data, establishing structure before visual grounding.
  • Rubric-guided GRPO: GRPO rewards final-answer correctness together with intermediate physical modeling and mathematical execution.Rubric-based scores evaluate the reasoning trajectory rather than only its final answer.
  • Reward design: The total reward combines rubric, outcome, and format rewards.Format validity requires the prescribed <plan>, <solution>, and <answer> structure.

F Experimental Setup

Experiments fine-tune three open-source vision-language models and evaluate them on diverse open-ended physics answers using a hybrid rule-based and LLM-assisted framework.

  • Training setup: SFT uses a text-only-to-multimodal curriculum, followed by GRPO from the multimodal SFT checkpoint.The setup uses LoRA for SFT and continues GRPO on multimodal physics data.
  • Base models: The evaluation uses Qwen2.5-VL-3B, Qwen2.5-VL-7B, and Qwen3-VL-8B as base vision-language models.These models span different scales and model series.
  • Answer evaluation: The evaluation framework supports numerical, symbolic, textual, and multiple-choice answers with specialized strategies.Numerical answers use value–unit normalization and tolerance checks, while symbolic answers use normalized symbolic equivalence.
  • Fallback evaluation: An LLM-based judge serves as a fallback when rule-based evaluation encounters parsing errors, unsupported formats, or ambiguity.This complements strict rule-based signals with coverage for variable open-ended answer forms.

H Analysis of Reflective Reasoning Behavior

The analysis examines reflective reasoning in sampled generations and contrasts baseline self-correction with structured physical modeling. Both approaches can reach the correct answer, but modeling organizes constraints before execution.

  • Qualitative Analysis: In the Atwood example, both the baseline and SFT cold start obtain the correct final speed of 4.43 m/s.The baseline first uses an incorrect intermediate sign convention, then recovers through reflective correction.
  • Qualitative Analysis: SFT cold start begins by constructing the physical system, making relevant constraints available before mathematical execution.The example suggests structured modeling can reduce the need for explicit self-revision.

I Qualitative Analysis

The qualitative examples illustrate structured modeling in coupled thermodynamic, electric-potential, and circuit problems. They emphasize organizing variables, constraints, and governing relations before numerical execution.

  • Carnot engine–refrigerator example: The Carnot engine–refrigerator example transfers the engine’s available work output coherently into the refrigerator stage.The setup uses ideal, reversible Carnot machines and determines Q3, the refrigerator’s extracted heat.
  • Electric potential-energy example: The electron problem models a downward uniform electric field, upward electron motion, force direction, field work, and potential-energy change as successive steps.The electron’s force is upward because its charge is negative, while the motion is upward through d = 520 m.
  • Kirchhoff circuit example: The circuit example represents three unknown currents and applies KCL at node c followed by KVL around two loops before solving the equation system.The modeling includes a constant-voltage battery, negligible wire resistance, and the relation I1 = I2 + I3.
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