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, differentiable physics, and AI for science. I'm advised by Rafael Gomez-Bombarelli.

Email / Scholar / Linkedin / Github

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
Paper

AtomSteer applies bounded, structure-dependent projections during sampling to steer protein-ligand cofolding, molecular conformers, and crystalline materials, without retraining or changing the model architecture.
It improves stereochemical accuracy, molecular geometry, physically valid docking success, and reconstruction of target space groups.

Pass@8 during RLVP post-training for 3B, 7B, and 14B models on the trained PDE families, with the Claude Opus 5 baseline.

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 | Project Page

RLVP trains LLMs to write PDE solvers using execution checks and continuous rewards for physical accuracy.

Multi-PDE post-training: One LLM is trained across eight PDE families using supervised fine-tuning followed by reinforcement learning.
With RLVP, 7B Qwen2.5-Coder reaches 68% pass@1 / 83% pass@8, outperforming Claude Opus 5 on the same PDE tasks under direct generation.
Transfer to unseen PDEs: Performance improves on some unseen equations, with evidence of transfer to 3D problems absent from 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

thermosetMC simulates cleavable polymer networks and predicts fragment molecular-weight distributions compared with experiments.

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

thermosetMC combines kinetic Monte Carlo simulations with experimental fragment data to infer crosslink density and reaction kinetics in degradable thermosets. It also predicts deconstruction outcomes.

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

Functional flow matching refines neural-operator predictions to support longer time rollouts.

Local attention improves long-term predictions from Fourier neural operators for multiscale PDEs and unstable reaction-diffusion problems.

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

Differentiable finite-element and spectral PDE solvers let us learn unknown physical terms through PDE-constrained optimization. We use this approach to infer cure kinetics in frontal polymerization.
Ongoing work: Learning PDE closure terms from thermal videos and calorimetry curves.

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 and graph neural networks guide an active-learning search for 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.