Pengfei Cai

I am a PhD candidate at MIT working in computational science and engineering, within the DMSE-CSE program. I work on post-training LLMs with verifiable physics, diffusion models with physical constraints, and AI for science. I'm advised by Rafael Gomez-Bombarelli.

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Pengfei Cai

Research
AtomSteer applies constraint projections during sampling to steer molecular conformers, crystalline materials, and protein-ligand complexes.
AtomSteer: Test-Time Constraint Steering for Atomistic Generative Models
Pengfei Cai*, Katharina Jäger*, Utkarsh Utkarsh, Nofit Segal, Bowen Deng, Akshay Subramanian, Rafael Gomez-Bombarelli
Under review
  • General framework for inference-time constraint steering of protein-ligand cofolding, molecular conformers, and crystalline materials, using bounded, structure-dependent projections without retraining or architectural changes.
  • Example demonstrations: Improves stereochemistry accuracy and molecular geometry, physically valid docking success, and target space group reconstruction, etc.
Pass@8 comparison of base, supervised fine-tuned, and RLVP models on the trained PDE families.
Reinforcement Learning with Verifiable Physics: Post-training LLMs with Continuous Rewards
Pengfei Cai*, Utkarsh Utkarsh*, Alan Edelman, Christopher Vincent Rackauckas, Rafael Gomez-Bombarelli
NeurIPS, 2026
Paper

RLVP turns simulations into an RL training environment, combining validity checks with continuous physical rewards.

  • Multi-PDE post-training: To our knowledge, the first SFT and RL pipeline to jointly post-train one LLM across diverse families of partial differential equations (PDEs).
  • RLVP on 7B Qwen2.5-Coder achieved 68% pass@1 / 83% pass@8, outperforming Claude Opus 5 on the same PDE tasks (direct generation).
  • Selective transfer: Evidence of improved code generation for unseen PDEs, including 3D problems never seen during post-training.
Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraints
Utkarsh*, Pengfei Cai*, Alan Edelman, Rafael Gomez-Bombarelli, Christopher Vincent Rackauckas
NeurIPS, 2025
Paper  |  Code  |  Project Page
Towards Long Rollout of Neural Operators with Local Attention and Flow Matching-inspired Correction: An Example in Frontal Polymerization PDEs
Pengfei Cai, Sulin Liu, Qibang Liu, Philippe Geubelle, Rafael Gomez-Bombarelli
NeurIPS 2024 Workshop on ML for Physical Sciences
  • Introduced functional flow matching for the refinement of predictions from neural operators to extend temporal roll-out.
  • Local attention-enhanced Fourier neural operators for improved long-term rollout of neural PDEs, especially for multiscale problems / reaction-diffusion PDEs with instabilities.
Learning Cure Kinetics of Frontal Polymerization PDEs using Differentiable Simulations
Pengfei Cai, Qibang Liu, Philippe Geubelle, Rafael Gomez-Bombarelli
ICML 2024 Workshop on AI for Science
NeurIPS 2024 Workshop on Data-driven and Differentiable Simulations, Surrogates, and Solvers
  • End-to-end learning of unknown physical terms in partial differential equations with differentiable PDE solvers (finite element or spectral methods). Here, by applying PDE-constrained optimization, we can learn cure kinetics terms in frontal polymerization processes.
  • Ongoing work: Learning closure terms in the PDE from multimodal experimental data (thermal capture videos and calorimetry curves).
Monte Carlo Simulation thermosetMC: Simulation and Fragment-Based Inference of Crosslink Density and Kinetics in Deconstructable Copolymer Thermosets
Pengfei Cai, Yuyan Wang, Adithya N. Sreenivasan, Kwangwook Ko, David J. Lundberg, Jeremiah A. Johnson, Rafael Gomez-Bombarelli
Under review at Macromolecules, 2026

Kinetic Monte Carlo framework for degradable thermoset materials, enabling fragment-based inference of crosslink density, reaction kinetics, and deconstruction outcomes from experimental fragment data.
Self-Improving Photosensitizer Discovery System via Bayesian Search with First-Principle Simulations
Shidang Xu*, Jiali Li*, Pengfei Cai, Xiaoli Liu, Bin Liu, Xiaonan Wang
Journal of the American Chemical Society, 2021
  • Bayesian optimization-based active learning and graph neural networks to accelerate the discovery of photosensitizer molecules.
Accelerated Design of Near-Infrared-II Molecular Fluorophores via First-Principle Understanding and Machine Learning
Shidang Xu*, Pengfei Cai*, Jiali Li, Xianhe Zhang, Xianglong Liu, Xiaonan Wang, Bin Liu
ChemRxiv 2022 Preprint
  • Virtual screening of NIR-II fluorophores with machine learning. Experimental validation underway.

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