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Shibo Li

Shibo Li contributes to research discovery and scholarly infrastructure.

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Published work

7 published item(s)

preprint2026arXiv

Multi-Fidelity Flow Matching: Cascaded Refinement of PDE Solutions

The source distribution in conditional flow matching is a design parameter that can be calibrated to data, not a default isotropic prior. We exploit this in Multi-Fidelity Flow Matching (MFFM), a cascade refinement framework for parametric PDE solutions: the source is calibrated to the empirical low-to-high-fidelity residual scale with local Gaussian-blur correlation, and the velocity network is conditioned on the low-fidelity solution. Conditioning makes the residual refinement problem substantially easier than unconditional field generation, while residual-calibrated source noise improves the flow-matching training geometry. A multi-resolution cascade applies the same construction independently between adjacent fidelities. After level-wise flow-matching pretraining, we fine-tune the composed cascade end-to-end with a deterministic one-step rollout, which makes one velocity evaluation per cascade level the optimized operating point at inference. The result is a learned analog of multigrid refinement that reaches the finest grid in $L$ deterministic network evaluations per query. We validate MFFM on eight benchmarks: two super-resolution problems and six spatiotemporal forecasting tasks from PDEBench, The Well, and the FNO Navier--Stokes dataset.

preprint2025arXiv

Dynamic Bayesian Optimization Framework for Instruction Tuning in Partial Differential Equation Discovery

Large Language Models (LLMs) show promise for equation discovery, yet their outputs are highly sensitive to prompt phrasing, a phenomenon we term instruction brittleness. Static prompts cannot adapt to the evolving state of a multi-step generation process, causing models to plateau at suboptimal solutions. To address this, we propose NeuroSymBO, which reframes prompt engineering as a sequential decision problem. Our method maintains a discrete library of reasoning strategies and uses Bayesian Optimization to select the optimal instruction at each step based on numerical feedback. Experiments on PDE discovery benchmarks show that adaptive instruction selection significantly outperforms fixed prompts, achieving higher recovery rates with more parsimonious solutions.

preprint2022arXiv

A novel learning-based robust model predictive control energy management strategy for fuel cell electric vehicles

The multi-source electromechanical coupling makes the energy management of fuel cell electric vehicles (FCEVs) relatively nonlinear and complex especially in the types of 4-wheel-drive (4WD) FCEVs. Accurate state observing for complicated nonlinear system is the basis for fantastic energy managing in FCEVs. Aiming at releasing the energy-saving potential of FCEVs, a novel learning-based robust model predictive control (LRMPC) strategy is proposed for a 4WD FCEV, contributing to suitable power distribution among multiple energy sources. The well-designed strategy based on machine learning (ML) translates the knowledge of the nonlinear system to the explicit controlling scheme with superior robust performance. To start with, ML methods with high regression accuracy and superior generalization ability are trained offline to establish the precise state observer for SOC. Then, explicit data tables for SOC generated by state observer are used for grabbing accurate state changing, whose input features include the vehicle status and the states of vehicle components. To be specific, the vehicle velocity estimation for providing future speed reference is constructed by deep forest. Next, the components including explicit data tables and vehicle velocity estimation are combined with model predictive control (MPC) to release the state-of-the-art energy-saving ability for the multi-freedom system in FCEVs, whose name is LRMPC. At last, the detailed assessment is performed in simulation test to validate the advancing performance of LRMPC. The corresponding results highlight the optimal control effect in energy-saving potential and strong real-time application ability of LRMPC.

preprint2022arXiv

A Self-Guided Framework for Radiology Report Generation

Automatic radiology report generation is essential to computer-aided diagnosis. Through the success of image captioning, medical report generation has been achievable. However, the lack of annotated disease labels is still the bottleneck of this area. In addition, the image-text data bias problem and complex sentences make it more difficult to generate accurate reports. To address these gaps, we pre-sent a self-guided framework (SGF), a suite of unsupervised and supervised deep learning methods to mimic the process of human learning and writing. In detail, our framework obtains the domain knowledge from medical reports with-out extra disease labels and guides itself to extract fined-grain visual features as-sociated with the text. Moreover, SGF successfully improves the accuracy and length of medical report generation by incorporating a similarity comparison mechanism that imitates the process of human self-improvement through compar-ative practice. Extensive experiments demonstrate the utility of our SGF in the majority of cases, showing its superior performance over state-of-the-art meth-ods. Our results highlight the capacity of the proposed framework to distinguish fined-grained visual details between words and verify its advantage in generating medical reports.

preprint2022arXiv

Nonparametric Embeddings of Sparse High-Order Interaction Events

High-order interaction events are common in real-world applications. Learning embeddings that encode the complex relationships of the participants from these events is of great importance in knowledge mining and predictive tasks. Despite the success of existing approaches, e.g. Poisson tensor factorization, they ignore the sparse structure underlying the data, namely the occurred interactions are far less than the possible interactions among all the participants. In this paper, we propose Nonparametric Embeddings of Sparse High-order interaction events (NESH). We hybridize a sparse hypergraph (tensor) process and a matrix Gaussian process to capture both the asymptotic structural sparsity within the interactions and nonlinear temporal relationships between the participants. We prove strong asymptotic bounds (including both a lower and an upper bound) of the sparsity ratio, which reveals the asymptotic properties of the sampled structure. We use batch-normalization, stick-breaking construction, and sparse variational GP approximations to develop an efficient, scalable model inference algorithm. We demonstrate the advantage of our approach in several real-world applications.

preprint2020arXiv

Analysis of Multivariate Scoring Functions for Automatic Unbiased Learning to Rank

Leveraging biased click data for optimizing learning to rank systems has been a popular approach in information retrieval. Because click data is often noisy and biased, a variety of methods have been proposed to construct unbiased learning to rank (ULTR) algorithms for the learning of unbiased ranking models. Among them, automatic unbiased learning to rank (AutoULTR) algorithms that jointly learn user bias models (i.e., propensity models) with unbiased rankers have received a lot of attention due to their superior performance and low deployment cost in practice. Despite their differences in theories and algorithm design, existing studies on ULTR usually use uni-variate ranking functions to score each document or result independently. On the other hand, recent advances in context-aware learning-to-rank models have shown that multivariate scoring functions, which read multiple documents together and predict their ranking scores jointly, are more powerful than uni-variate ranking functions in ranking tasks with human-annotated relevance labels. Whether such superior performance would hold in ULTR with noisy data, however, is mostly unknown. In this paper, we investigate existing multivariate scoring functions and AutoULTR algorithms in theory and prove that permutation invariance is a crucial factor that determines whether a context-aware learning-to-rank model could be applied to existing AutoULTR framework. Our experiments with synthetic clicks on two large-scale benchmark datasets show that AutoULTR models with permutation-invariant multivariate scoring functions significantly outperform those with uni-variate scoring functions and permutation-variant multivariate scoring functions.

preprint2020arXiv

Scalable Variational Gaussian Process Regression Networks

Gaussian process regression networks (GPRN) are powerful Bayesian models for multi-output regression, but their inference is intractable. To address this issue, existing methods use a fully factorized structure (or a mixture of such structures) over all the outputs and latent functions for posterior approximation, which, however, can miss the strong posterior dependencies among the latent variables and hurt the inference quality. In addition, the updates of the variational parameters are inefficient and can be prohibitively expensive for a large number of outputs. To overcome these limitations, we propose a scalable variational inference algorithm for GPRN, which not only captures the abundant posterior dependencies but also is much more efficient for massive outputs. We tensorize the output space and introduce tensor/matrix-normal variational posteriors to capture the posterior correlations and to reduce the parameters. We jointly optimize all the parameters and exploit the inherent Kronecker product structure in the variational model evidence lower bound to accelerate the computation. We demonstrate the advantages of our method in several real-world applications.