PHYRD: A Living Benchmark for Reproducing and Extending Theoretical Physics Research
Organizations: EPIC Lab, Shanghai Jiao Tong University · Fudan University · University of Electronic Science and Technology of China · University of Science and Technology of China
Abstract
Large language models and agents have shown significant power in advanced physical research. In this paper, We introduce PHYRD, a living benchmark for theoretical-physics reasoning with 63 Reproduce and 43 Discover problems. Reproduce tests derivation of published results; Discover tests consequences of modified theoretical conditions. FormulaForest constructs the tasks with reference solutions and subquestion-level rubrics. Across five models, whole-problem accuracy ranges from 49.21% to 68.25% on Reproduce and from 18.60% to 74.42% on closed-book Discover. With tools, four models complete more Discover problems, but conceptual errors and missing arguments persist. Besides, our experimental results demonstrate the value of FormulaForest as synthetic data. On FrontierScience, a benchmark developed by OpenAI, it raises the accuracy of a Qwen-35B-A3B model from 61% to 72%.
Figures & tables
| Benchmark | Physics focus | Tool use | Research tasks | Derivation under modified conditions | Continued expansion |
|---|---|---|---|---|---|
| MATH | ✗ | ✗ | ✗ | ✗ | ✗ |
| ScienceAgentBench | ✗ | ✓ | ✓ | — | — |
| PRL-Bench | ✓ | ✓ | ✓ | — | ✓ |
| HorizonMath | ✗ | — | ✓ | — | ✓ |
| MathArena | ✗ | ✓ | ✓ | — | ✓ |
| LiveBench | ✗ | ✗ | ✗ | ✗ | ✓ |
Appendix figures & tables14 assets
Supplementary material from the paper’s appendix.
Appendix
| Track | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Total |
|---|---|---|---|---|---|---|---|---|
| Reproduce | 1 | 39 | 20 | 2 | 0 | 1 | 0 | 63 |
| Discover | 3 | 6 | 22 | 7 | 2 | 1 | 2 | 43 |
| Matrix | Pole order | Coefficient ranks | Power growth |
|---|---|---|---|
| 1 | bounded | ||
| 2 | |||
| 4 |
| ID | Field | Task / source | |
|---|---|---|---|
| A001 | Cond-Mat | Static Aristotelian algebra sector (R01) | 5 |
| A003 | Cond-Mat | Post coupling variation in dipole Noether gauging (R01) | 4 |
| A004 | Cond-Mat | Dilatation algebra sector (R01) | 4 |
| A009 | Stat | Logarithmic boundary entropy in the deformed Ising model (R02) | 4 |
| A010 | Cond-Mat | Spatial symmetries in a fracton scalar theory (R01) | 5 |
| A011 | Cond-Mat | Dipole algebra sector (R01) | 4 |
| Key | Source title and identifier |
|---|---|
| R01 | Fractons, dipole symmetries and curved spacetime. https://doi.org/10.21468/scipostphys.12.6.205 |
| R02 | -deformed 2D quantum field theories. https://doi.org/10.1007/jhep10(2016)112 |
| R03 | Moving the CFT into the bulk with . https://doi.org/10.1007/jhep04(2018)010 |
| R04 | Lieb-Schultz-Mattis, Luttinger, and ’t Hooft - anomaly matching in lattice systems. https://doi.org/10.21468/scipostphys.15.2.051 |
| R05 | Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings. https://doi.org/10.1088/1361-6382/aaa3a8 |
| R06 | The IR-resummed Effective Field Theory of Large Scale Structures. https://doi.org/10.1088/1475-7516/2015/02/013 |
| ID | Field | Source paper (arXiv identifier) | |
|---|---|---|---|
| p01 | Astro | Quantum de Sitter and Analytically-Continued Chern–Simons Theory (2608.07467) | 4 |
| p02 | Quantum | Solvable Renyi Indices in Critical Stabilizer Entropy: From Cauchy Minors to Discrete Selberg Sums (2608.06995) | 5 |
| p03 | HEP | Bootstrapping 3D Conformal Field Theories with Product Analytic Functionals (2608.06497) | 3 |
| p05 | Quantum | Spectral Topology and Universal Krylov Dynamics (2608.07258) | 3 |
| p06 | Astro | Formation of the Kerr black hole: an exact model (2608.06519) | 4 |
| p07 | HEP | Topological defects in reflection positive topological field theories (2608.07217) | 6 |
| SAcc | GPT | DeepSeek | GLM | Kimi | Qwen |
|---|---|---|---|---|---|
| Astro | 91.00 | 86.83 | 93.33 | 94.17 | 89.33 |
| CM | 91.88 | 85.62 | 80.00 | 65.00 | 88.12 |
| HEP | 87.05 | 88.33 | 81.37 | 81.45 | 82.76 |
| Qtm | 75.00 | 83.33 | 70.00 | 60.00 | 86.67 |
| Stat | 100.00 | 75.00 | 75.00 | 66.67 | 75.00 |
| All | 88.33 | 86.88 | 82.25 | 79.66 | 84.30 |
| SAcc | GPT | DeepSeek | GLM | Kimi | Qwen |
|---|---|---|---|---|---|
| Astro | 97.78 | 82.78 | 61.11 | 55.00 | 36.11 |
| CM | 93.33 | 85.00 | 60.00 | 74.17 | 49.17 |
| HEP | 86.33 | 77.12 | 59.52 | 59.93 | 54.20 |
| Qtm | 91.43 | 91.90 | 58.10 | 68.73 | 90.32 |
| Stat | 97.22 | 92.22 | 56.11 | 82.22 | 71.94 |
| All | 91.06 | 82.67 | 59.34 | 63.40 | 57.59 |
| SAcc | GPT | DeepSeek | GLM | Kimi | Qwen |
|---|---|---|---|---|---|
| Astro | 97.78 | 82.78 | 68.33 | 71.11 | 71.67 |
| CM | 95.83 | 78.33 | 56.67 | 80.00 | 60.83 |
| HEP | 93.67 | 93.00 | 63.80 | 72.02 | 65.61 |
| Qtm | 97.14 | 100.00 | 87.30 | 82.54 | 88.10 |
| Stat | 92.22 | 100.00 | 78.33 | 75.42 | 83.75 |
| All | 95.11 | 91.63 | 69.43 | 74.42 | 71.89 |
| Model | C | D | A | I | Total |
|---|---|---|---|---|---|
| Reproduce | |||||
| GPT-5.6 Sol | 4 | 0 | 7 | 20 | 31 |
| DeepSeek v4 Pro | 12 | 2 | 11 | 10 | 35 |
| GLM-5.2 | 11 | 3 | 29 | 4 | 47 |
| Kimi K2.6 | 24 | 2 | 24 | 4 | 54 |
| Qwen3.7-Max | 19 | 3 | 13 | 9 | 44 |
Scientific Reasoning in Language Models
Scientific reasoning in language models studies how AI systems use evidence, domain knowledge, and tools to solve problems and support discovery.
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