About

Ruimeng Hu is a faculty member in the Department of Mathematics at the University of California, Santa Barbara. His research specialization includes Machine Learning, Financial Mathematics, Stochastic Control and Games, and Mean Field Approximation. He is based in South Hall, Room 6607, and maintains office hours from Monday to Friday, 9-12 and 1-4. His contact email is rhu@math.ucsb.edu, and his professional webpage is https://sites.google.com/site/ruimenghu1/. The department and university provide additional resources and support for his academic activities.

Research topics

• Artificial Intelligence
• Computer Science
• Mathematics
• Medicine
• Algorithm
• Applied mathematics
• Mathematical economics
• Mathematical optimization

Selected publications

• Convergence Analysis of PINNs for Fractional Diffusion Equations in Bounded Domains

  ArXiv.org · 2026-01-04

  articleOpen access

  We establish the convergence of physics-informed neural networks (PINNs) for time-dependent fractional diffusion equations posed on bounded domains. The presence of fractional Laplacian operators introduces nonlocal behavior and regularity constraints, and standard neural network approximations do not naturally enforce the associated spectral boundary conditions. To address this challenge, we introduce a spectrally-defined mollification strategy that preserves the structure of the nonlocal operator while ensuring boundary compatibility. This enables the derivation of rigorous energy estimates in Sobolev spaces. Our results rely on analytical tools from PDE theory, highlighting the compatibility of PINN approximations with classical energy estimates for nonlocal equations. We prove convergence of the PINN approximation in any space-time Sobolev norm $H^k$ (with $k \in \N)$. The analysis highlights the role of mollified residuals in enabling theoretical guarantees for neural-network-based solvers of nonlocal PDEs.

  PublisherOA PDF

• Deception in Linear-Quadratic Control

  arXiv (Cornell University) · 2026-03-31

  preprintOpen access

  Systems operating in adversarial environments may inadvertently leak sensitive information to adversaries. To address this challenge, we revisit the linear-quadratic control framework and introduce deception to actively mislead adversaries. Specifically, we consider a blue-team agent, observed by a red-team agent, that seeks to minimize a quadratic cost while introducing perturbations to its trajectories over time. These perturbations are designed to corrupt the red team's observations and, consequently, any downstream inferences, while remaining undetected by a red team using sequential hypothesis testing. We implement this idea by augmenting the blue team's quadratic cost with a likelihood ratio statistic. Under this augmented control problem, we derive a semi-explicit solution for the optimal deceptive control law and establish corresponding well-posedness results. In addition, we provide both numerical approximations and analytical bounds for the probability that the red team detects the blue team's deceptive strategies. Numerical results demonstrate the effectiveness of the proposed framework in deceiving the red team while remaining undetected with probability near 1.

  PublisherDOI

• Convergence Analysis of PINNs for Fractional Diffusion Equations in Bounded Domains

  arXiv (Cornell University) · 2026-01-04

  preprintOpen access

  We establish the convergence of physics-informed neural networks (PINNs) for time-dependent fractional diffusion equations posed on bounded domains. The presence of fractional Laplacian operators introduces nonlocal behavior and regularity constraints, and standard neural network approximations do not naturally enforce the associated spectral boundary conditions. To address this challenge, we introduce a spectrally-defined mollification strategy that preserves the structure of the nonlocal operator while ensuring boundary compatibility. This enables the derivation of rigorous energy estimates in Sobolev spaces. Our results rely on analytical tools from PDE theory, highlighting the compatibility of PINN approximations with classical energy estimates for nonlocal equations. We prove convergence of the PINN approximation in any space-time Sobolev norm $H^k$ (with $k \in \N)$. The analysis highlights the role of mollified residuals in enabling theoretical guarantees for neural-network-based solvers of nonlocal PDEs.

  PublisherDOI

• Replication Materials for Article: Two-Time-Scale Transfer Learning for Market-by-Order Micro-Return Forecasting

  Zenodo (CERN European Organization for Nuclear Research) · 2026-03-17

  datasetOpen accessSenior author

  This archive contains the replication artifacts, including experimental logs, output data, and the synthetic dataset, for the paper "Two-Time-Scale Transfer Learning for Market-by-Order Micro-Return Forecasting". Paper Abstract Deep Learning models face a critical "simulation-to-reality" gap when applied to high frequency financial data. Deep learning models often fail to capture the non-stationary dynamics of live markets, requiring computationally expensive recalibrations. This work introduces the Two-Time-Scale Transfer Learning (TTSTL) framework, a hybrid model architecture that combines the flexibility of deep learning models with the parsimony and calibration ease of time series regression models. The TTSTL architecture mimics the hippocampus-neocortex interaction in the human brain by coupling a high-capacity deep learning "backbone" with a lightweight, adaptive time series regression "adapter." The backbone, utilizing a CNN-LSTM network, extracts complex, non-linear feature interactions from event-driven limit order book data, while the adapter—implemented as a Hybrid ARMAX-GARCH-DeepLOB model—integrates these features into a statistical framework for micro-return forecasting. Experiments are conducted on synthetic and Intel (INTC) market-by-order data. Results demonstrate that the TTSTL framework significantly outperforms standalone deep learning baselines in terms of accuracy (RelMAE), while enabling volatility modeling and formal probabilistic forecasting. Usage This dataset facilitates the reproduction of the results presented in the paper. The code required to process this data and run the experiments is hosted on GitHub. Repositories Main Codebase (Models & Experiments):https://github.com/judmejiabe/ttstl_repoContains the TTSTL framework implementation, experimental scripts, and analysis tools. Data Pipeline (Generation & Processing):https://github.com/judmejiabe/evolving-microstructural-toolkit-dataContains the scripts for generating the synthetic data and processing the real market data. Installation Instructions Clone the Main Codebase repository. Follow the installation instructions in the README.md file (local install or Docker). Download this Zenodo dataset. For Synthetic Data: Unzip the Recorded_Synthetic_Data contents into the data.nosync/Recorded_Synthetic_Data directory at the root of the Data Pipeline repository structure if you wish to run the generation scripts, or configure the paths in the Main Codebase to point to the extracted files. For Logs and Outputs: The logs/ and outputs/ directories in this archive directly correspond to the directory structure generated by the experiments in the Main Codebase. You can place them in the root of the cloned ttstl_repo to analyze the results without re-running the heavy computations. Files Included 1. Logs Directory (logs/) Contains execution logs for pretraining, experiments, and tests. cnn_lstm_pretraining_future_20260120_110456.log: Log of the CNN-LSTM feature extractor pretraining on May 2024 INTC data. Captures training loss, validation loss, and model checkpointing for the "future returns" prediction task. market_data_experiments_future_20251203_152025.log: Log of the main market data experiments. Records the Orchestrator's progress through recursive forecasting windows (backbone bars, stacks, adapter bars) and performance metrics for the future returns task. synthetic_study_20251114_154826.log: Log of the synthetic study experiments. Details the execution of 28 configurations (combinations of update rules and covariate sets) on synthetic LOB data. 2. Outputs Directory (outputs/) Contains data products, trained models, and analysis results. Analysis Results Market Data Analysis (outputs/analysis_market_data_experiment_results/): sequential_boxplot_*.png: Visualization of performance metrics (MAE, RMSE) over time across recursive updates. *_aggregate_*.png: Boxplots showing the distribution of covariates (OFI, VIX) and their statistics. comparison_stacked_by_pair.csv: Aggregated performance metrics comparing the TTSTL model against baselines. Synthetic Study Analysis (outputs/analysis_synthetic_data_experiment_results/): Contains tables showing the relative performance ranking of different update methods and RelMAE plots across simulation scenarios. Pretrained Models Artifacts for the pretrained CNN-LSTM feature extractor used in the market data experiments (outputs/cnn_lstm_pretraining_market_data/): *.pth: PyTorch model weights. *_scaler.pkl: Serialized StandardScaler fitted on the pretraining data. *_bounds.json: JSON file containing winsorization bounds. *_metadata.json: Metadata describing the training configuration. *_training_history.csv: CSV log of training and validation loss per epoch. Experiment Runs Raw outputs from the recursive market data experiments (outputs/runs_market_data_experiments/) and synthetic study (outputs/runs_synthetic_study/). Organized hierarchically by Date, Configuration, Backbone Bar, Stack, and Adapter. config.yaml: Configuration snapshot for the specific run. performance.parquet: Detailed frame-by-frame performance metrics (MAE, MSE, R2). forecasts.parquet: Time-series of predicted vs. actual micro-returns. model_state.pth: Snapshots of the adapter model state (if saved). 3. Recorded Synthetic Data (data/Recorded_Synthetic_Data/) The raw event-driven and physical time-driven synthetic LOB data used for the controlled study. *_event_driven_recorded_lob_*.parquet: Event-driven snapshots used for model training/updates. *_physical_time_driven_recorded_data_*.parquet: Physical time snapshots used for calculating micro-returns (targets). Citation If you use this dataset or code in your research, please cite the working paper: @article{mejiabecerra2026twotimescale, title = {Two-Time-Scale Transfer Learning for Market-by-Order Micro-Return Forecasting}, author = {Mejia Becerra, Juan Diego and Peters, Gareth W. and Hu, Ruimeng}, year = {2026}, journal = {SSRN Electronic Journal}, doi = {10.2139/ssrn.6424798}, url = {https://ssrn.com/abstract=6424798} }

  PublisherDOI

• Two-Time-Scale Transfer Learning for Market-by-Order Micro-Return Forecasting

  SSRN Electronic Journal · 2026-01-01

  preprintOpen accessSenior author
  PublisherDOI

• Information Revelation and Alignment Faking in Stochastic Differential Games

  ArXiv.org · 2026-03-17

  articleOpen accessSenior author

  In competitive games with private objectives, actions can reveal information about hidden parameters. Quantifying such information revelation, however, is substantially more challenging, since it depends not only on the opponent's hidden parameter but also on the opponent's model of the game. We study this problem via a two-player linear-quadratic stochastic differential game under partial information, in which each player knows its own coupling parameter and models the opponent's hidden parameter through a prior. Starting from the full-information game, we characterize the Nash equilibrium by coupled Riccati equations. We then define baseline implementable controls by averaging the equilibrium under each player's prior. Building on this baseline, we formulate an alignment-faking control problem in which one player trades off fidelity to its implementable policy against information acquisition about the opponent's hidden parameter. The information incentive is constructed from a proxy Fisher information matrix based only on the player's available model. This leads to a tractable saddle-point formulation with semi-explicit control characterization through Riccati systems. Numerical illustrations show that alignment faking can substantially improve information gain over baseline play when the faker's model is accurate, but often at the cost of greater detectability. They also show that the proxy Fisher information can systematically differ from the true information under model misspecification.

  PublisherOA PDF

• Modeling Stochastic Multi-Agent Interaction in Intraday Battery Energy Storage Dispatch with Market Power

  ArXiv.org · 2026-05-02

  articleOpen access1st authorCorresponding

  We develop a stochastic game-theoretic model for intraday dispatch of grid-scale battery energy storage systems (BESSs). We assume that each BESS operator competitively manages her state-of-charge to maximize energy arbitrage revenues, driven by the endogenized electricity price that depends on the sum of the charging rates. We characterize the Nash equilibrium of the resulting finite-player linear-quadratic differential game with a shared stochastic driver, obtaining semi-explicit representations of equilibrium feedback controls and equilibrium prices both in the general heterogeneous and the simplified homogeneous BESS setting, via a system of Riccati equations. We then analyze competitive effects, including the marginal externality of additional BESS entering the market, the benefit of coordination and the corresponding market power of large operators, and supply effects from hybrid-type BESSs. We further study the asymptotic regime as the number of agents grows large. Our model provides a quantitative testbed to study the impact of decentralized BESS deployment on the grid and the resulting reduction in daily price spreads.

  PublisherOA PDF

• Replication Materials for Article: Two-Time-Scale Transfer Learning for Market-by-Order Micro-Return Forecasting

  Zenodo (CERN European Organization for Nuclear Research) · 2026-03-17

  datasetOpen accessSenior author

  This archive contains the replication artifacts, including experimental logs, output data, and the synthetic dataset, for the paper "Two-Time-Scale Transfer Learning for Market-by-Order Micro-Return Forecasting". Paper Abstract Deep Learning models face a critical "simulation-to-reality" gap when applied to high frequency financial data. Deep learning models often fail to capture the non-stationary dynamics of live markets, requiring computationally expensive recalibrations. This work introduces the Two-Time-Scale Transfer Learning (TTSTL) framework, a hybrid model architecture that combines the flexibility of deep learning models with the parsimony and calibration ease of time series regression models. The TTSTL architecture mimics the hippocampus-neocortex interaction in the human brain by coupling a high-capacity deep learning "backbone" with a lightweight, adaptive time series regression "adapter." The backbone, utilizing a CNN-LSTM network, extracts complex, non-linear feature interactions from event-driven limit order book data, while the adapter—implemented as a Hybrid ARMAX-GARCH-DeepLOB model—integrates these features into a statistical framework for micro-return forecasting. Experiments are conducted on synthetic and Intel (INTC) market-by-order data. Results demonstrate that the TTSTL framework significantly outperforms standalone deep learning baselines in terms of accuracy (RelMAE), while enabling volatility modeling and formal probabilistic forecasting. Usage This dataset facilitates the reproduction of the results presented in the paper. The code required to process this data and run the experiments is hosted on GitHub. Repositories Main Codebase (Models & Experiments):https://github.com/judmejiabe/ttstl_repoContains the TTSTL framework implementation, experimental scripts, and analysis tools. Data Pipeline (Generation & Processing):https://github.com/judmejiabe/evolving-microstructural-toolkit-dataContains the scripts for generating the synthetic data and processing the real market data. Installation Instructions Clone the Main Codebase repository. Follow the installation instructions in the README.md file (local install or Docker). Download this Zenodo dataset. For Synthetic Data: Unzip the Recorded_Synthetic_Data contents into the data.nosync/Recorded_Synthetic_Data directory at the root of the Data Pipeline repository structure if you wish to run the generation scripts, or configure the paths in the Main Codebase to point to the extracted files. For Logs and Outputs: The logs/ and outputs/ directories in this archive directly correspond to the directory structure generated by the experiments in the Main Codebase. You can place them in the root of the cloned ttstl_repo to analyze the results without re-running the heavy computations. Files Included 1. Logs Directory (logs/) Contains execution logs for pretraining, experiments, and tests. cnn_lstm_pretraining_future_20260120_110456.log: Log of the CNN-LSTM feature extractor pretraining on May 2024 INTC data. Captures training loss, validation loss, and model checkpointing for the "future returns" prediction task. market_data_experiments_future_20251203_152025.log: Log of the main market data experiments. Records the Orchestrator's progress through recursive forecasting windows (backbone bars, stacks, adapter bars) and performance metrics for the future returns task. synthetic_study_20251114_154826.log: Log of the synthetic study experiments. Details the execution of 28 configurations (combinations of update rules and covariate sets) on synthetic LOB data. 2. Outputs Directory (outputs/) Contains data products, trained models, and analysis results. Analysis Results Market Data Analysis (outputs/analysis_market_data_experiment_results/): sequential_boxplot_*.png: Visualization of performance metrics (MAE, RMSE) over time across recursive updates. *_aggregate_*.png: Boxplots showing the distribution of covariates (OFI, VIX) and their statistics. comparison_stacked_by_pair.csv: Aggregated performance metrics comparing the TTSTL model against baselines. Synthetic Study Analysis (outputs/analysis_synthetic_data_experiment_results/): Contains tables showing the relative performance ranking of different update methods and RelMAE plots across simulation scenarios. Pretrained Models Artifacts for the pretrained CNN-LSTM feature extractor used in the market data experiments (outputs/cnn_lstm_pretraining_market_data/): *.pth: PyTorch model weights. *_scaler.pkl: Serialized StandardScaler fitted on the pretraining data. *_bounds.json: JSON file containing winsorization bounds. *_metadata.json: Metadata describing the training configuration. *_training_history.csv: CSV log of training and validation loss per epoch. Experiment Runs Raw outputs from the recursive market data experiments (outputs/runs_market_data_experiments/) and synthetic study (outputs/runs_synthetic_study/). Organized hierarchically by Date, Configuration, Backbone Bar, Stack, and Adapter. config.yaml: Configuration snapshot for the specific run. performance.parquet: Detailed frame-by-frame performance metrics (MAE, MSE, R2). forecasts.parquet: Time-series of predicted vs. actual micro-returns. model_state.pth: Snapshots of the adapter model state (if saved). 3. Recorded Synthetic Data (data/Recorded_Synthetic_Data/) The raw event-driven and physical time-driven synthetic LOB data used for the controlled study. *_event_driven_recorded_lob_*.parquet: Event-driven snapshots used for model training/updates. *_physical_time_driven_recorded_data_*.parquet: Physical time snapshots used for calculating micro-returns (targets). Citation If you use this dataset or code in your research, please cite the working paper: @article{mejiabecerra2026twotimescale, title = {Two-Time-Scale Transfer Learning for Market-by-Order Micro-Return Forecasting}, author = {Mejia Becerra, Juan Diego and Peters, Gareth W. and Hu, Ruimeng}, year = {2026}, journal = {SSRN Electronic Journal}, doi = {10.2139/ssrn.6424798}, url = {https://ssrn.com/abstract=6424798} }

  PublisherDOI

• An Actor-Critic Framework for Continuous-Time Jump-Diffusion Controls with Normalizing Flows

  arXiv (Cornell University) · 2026-04-07

  preprintOpen access

  Continuous-time stochastic control with time-inhomogeneous jump-diffusion dynamics is central in finance and economics, but computing optimal policies is difficult under explicit time dependence, discontinuous shocks, and high dimensionality. We propose an actor-critic framework that serves as a mesh-free solver for entropy-regularized control problems and stochastic games with jumps. The approach is built on a time-inhomogeneous little q-function and an appropriate occupation measure, yielding a policy-gradient representation that accommodates time-dependent drift, volatility, and jump terms. To represent expressive stochastic policies in continuous-action spaces, we parameterize the actor using conditional normalizing flows, enabling flexible non-Gaussian policies while retaining exact likelihood evaluation for entropy regularization and policy optimization. We validate the method on time-inhomogeneous linear-quadratic control, Merton portfolio optimization, and a multi-agent portfolio game, using explicit solutions or high-accuracy benchmarks. Numerical results demonstrate stable learning under jump discontinuities, accurate approximation of optimal stochastic policies, and favorable scaling with respect to dimension and number of agents.

  PublisherDOI

• Deception in Linear-Quadratic Control

  ArXiv.org · 2026-03-31

  articleOpen access

  Systems operating in adversarial environments may inadvertently leak sensitive information to adversaries. To address this challenge, we revisit the linear-quadratic control framework and introduce deception to actively mislead adversaries. Specifically, we consider a blue-team agent, observed by a red-team agent, that seeks to minimize a quadratic cost while introducing perturbations to its trajectories over time. These perturbations are designed to corrupt the red team's observations and, consequently, any downstream inferences, while remaining undetected by a red team using sequential hypothesis testing. We implement this idea by augmenting the blue team's quadratic cost with a likelihood ratio statistic. Under this augmented control problem, we derive a semi-explicit solution for the optimal deceptive control law and establish corresponding well-posedness results. In addition, we provide both numerical approximations and analytical bounds for the probability that the red team detects the blue team's deceptive strategies. Numerical results demonstrate the effectiveness of the proposed framework in deceiving the red team while remaining undetected with probability near 1.

  PublisherOA PDF

Recent grants

• Collaborative Research: Machine Learning Theory and Algorithms for Differential Games, with Applications in Economics

  NSF · $200k · 2020–2023

Frequent coauthors

• Jean‐Pierre Fouque

  21 shared

• Jiequn Han

  Flatiron Health (United States)

  19 shared

• Quyuan Lin

  9 shared

• Jihao Long

  Princeton University

  7 shared

• Robert Balkin

  University of California, Santa Barbara

  5 shared

• Ming Min

  University of California, Santa Barbara

  4 shared

• Elie Abdo

  Snam (Italy)

  4 shared

• Héctor D. Ceniceros

  University of California, Santa Barbara

  4 shared

Education

• Ph.D., Statistics and Applied Probability

  University of California, Santa Barbara

  2018

• B.S., Mathematics

  Peking University

  2012