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Feng Bao

Publications and source records attributed to Feng Bao.

At least 19 recordsLinked to original sources
arXiv2026

Purcell-Engineered Hybrid Coupler for Leakage-Suppressed Robust CZ Gates

We propose a Purcell-engineered notch-filter hybrid coupler for superconducting controlled-$Z$ (CZ) gates that combines coherent interaction engineering with leakage-selective dissipation. The architecture integrates a nonlinear transmon coupler with a coupled Purcell-filter and notch-resonator subsystem, providing additional control over both the coherent interaction pathways and the engineered dissipative environment. The filter branch reshapes the effective interaction pathways, while the notch resonator further tailors the frequency response of the coupled filter network and preserves strong leakage-selective dissipation. Using dressed-eigenstate analysis together with Lindblad master-equation simulations, we show that the proposed architecture substantially reduces leakage and improves the worst-case computational-state fidelity compared with an optimized single-transmon coupler while remaining robust over a broad range of coherence assumptions and device parameters. The optimized gate achieves $F_{\rm avg}=99.74\%$, $F_{\rm min}=99.62\%$, and a maximum leakage probability of $1.6\times10^{-3}$. These results demonstrate that engineered dissipation complements conventional coherent interaction engineering and provides an additional design degree of freedom for realizing robust, high-fidelity superconducting CZ gates.

quant-ph↗
arXiv2026

A Two-Step Ensemble Score Filter for Data Assimilation in Partially Observed Systems

Data assimilation blends model forecasts with observations to estimate the evolving state of complex dynamical systems, but sparse observing networks remain challenging because unobserved state variables are not directly constrained by observations. In this work, we introduce the Ensemble Score Filter with Linear Regression (EnSF-LR), a two-step filtering method for partially observed nonlinear systems. At each analysis time, EnSF-LR first applies the Ensemble Score Filter (EnSF) to update the observed state components using a nonlinear score-based analysis update. It then computes the resulting observed-state analysis increments and maps these corrections to the unobserved components through the ensemble-based prior covariance matrix. The latter amounts to the same linear regression mechanism used by Ensemble Kalman Filters (EnKFs). We evaluate EnSF-LR using the Lorenz-63 and 40-dimensional Lorenz-96 systems with sparse linear and nonlinear observations. The method is compared with the original EnSF and with the classical stochastic EnKF. In the linear-observation experiments, EnSF-LR produces accuracy comparable to the EnKF baseline while substantially reducing error relative to the original EnSF. In the nonlinear-observation experiments, EnSF-LR achieves lower full-state root-mean-square error than both the original EnSF and the EnKF reference. These results suggest that hybridizing score-based and EnKF analysis schemes provides an effective strategy for assimilating sparse and nonlinear observations.

physics.ao-ph↗
arXiv2026

Diffusion Model-Based Data Assimilation for Real-World Energy Consumption Forecasting

Accurate estimation and forecasting of energy consumption are important for power-system operation, planning, and demand-side management. In practice, however, complete and timely measurements may not always be available, and the observed data can be partial, noisy, or delayed. This motivates the use of learned forecasting models for predicting the evolving consumption state, together with data assimilation methods for sequential forecast correction. In this work, we study a high-dimensional data assimilation problem for real energy-consumption data. \modeltext{The forward prediction is supplied by a pretrained black-box spatio-temporal forecasting model, which is treated as the state propagator in the filtering procedure.} We employ the Ensemble Score Filter (EnSF) to assimilate partial and noisy observations and to correct the forecast trajectory over time. The EnSF uses score-based diffusion models to approximate filtering distributions and avoids retraining neural-network score models during assimilation by using a closed-form score representation and Monte Carlo approximation. Numerical experiments demonstrate that open-loop propagation of the learned forecasting model can become unreliable over long horizons, while EnSF-based correction substantially improves state estimation. Comparisons with the Ensemble Kalman Filter (EnKF) further show that EnSF provides stronger correction under the nonlinear observation setting considered in this work.

cs.LG↗
arXiv2026

Diffusion-Based Stochastic Operator Networks for Uncertainty Quantification in Stochastic Partial Differential Equations

We introduce a novel framework for uncertainty quantification of solution operators associated with stochastic partial differential equations (SPDEs). Although SPDEs play a central role in modeling complex physical systems under uncertainty, their practical use typically requires specifying the magnitude and structure of model uncertainties that are often unknown and difficult to infer from noisy measurements. To address this challenge, we develop a stochastic operator-learning framework that learns directly from noisy data and outputs both a mean solution field and a quantification of uncertainty. The proposed method, namely the Stochastic Operator Network (SON), is constructed by combining the structure of the Deep Operator Network (DeepONet) with Stochastic Neural Networks (SNNs) to model stochasticity and enable probabilistic prediction. The training procedure is carried out by minimizing a Hamiltonian-type loss and optimizing the resulting objective using the Stochastic Maximum Principle. Numerical experiments on benchmark SPDEs under multiple uncertainty sources demonstrate the accuracy and robustness of the proposed method in capturing solution structure and quantifying predictive uncertainty.

stat.ML↗
arXiv2026

Finite Expression Method with TranNet-based Function Learning for High-Dimensional Partial Differential Equations

In this paper, we study a machine-learning-based solver for high-dimensional partial differential equations (PDEs). Computing accurate solutions efficiently for such problems remains challenging because of the curse of dimensionality, which severely limits the scalability of classical numerical methods. Our approach builds on the recently developed finite expression method (FEX), which approximates PDE solutions in a function space generated by finitely many analytic expressions. This framework has been shown to achieve high, and in some cases machine-level, accuracy with polynomial memory complexity and favorable computational cost. We propose an extension of FEX in which the functional pool is generated by shallow neural network operators whose parameters are initialized using the transferable neural network method TransNet. Numerical experiments suggest that the proposed extension is an effective alternative for solving several high-dimensional PDEs.

math.NA↗
arXiv2026

Fully multiplexed photonic tensor computing

Tensor operations dominate modern computational workloads, yet their further acceleration demands hardware platforms with greater parallelism. Although photonic computing provides a compelling route for parallel processing, fully exploiting all native multiplexing dimensions of optical fields is impeded by the challenges in routing and programming light in all dimensions simultaneously. Here we introduce FieldCore, a fully multiplexed photonic tensor core that jointly harnesses wavelength, radio-frequency, guided-mode, time and space dimensions, thereby enabling parallelism to scale multiplicatively within a single optical field. Enabled by inverse-designed silicon photonics, FieldCore preserves a uniform programmed computation across all multiplexed channels in parallel. Experimentally, we validate and benchmark its performance from ultra-high-baudrate arithmetic operations to high-fidelity image convolution and parallel handwritten-digit recognition. We further use FieldCore to unlock applications that naturally require high-dimensional data processing, such as high-dimensional hyperspectral classification and massively parallel mechanical fault diagnosis. Our FieldCore supports an estimated aggregate compute throughput of 69.12 tera operations per second (TOPS) and accommodates up to 1,800 parallel input streams within a single core, establishing a scalable paradigm for fully multiplexed photonic tensor computing and AI inference.

physics.optics↗
arXiv2026

Global Attention with Linear Complexity for Exascale Generative Data Assimilation in Earth System Prediction

Accurate Earth system prediction requires state inference from incomplete observations, but conventional two-stage data assimilation (DA) is computationally prohibitive because repeated PDE-based ensemble forecasts, observation updates, and intermediate data movement limit ensemble size at high resolution. We introduce STORM, a one-stage generative AI framework that reformulates DA as diffusion-based Bayesian posterior sampling, replacing online PDE ensemble forecasts with scalable AI inference. It further combines a spatiotemporal transformer with a global-attention algorithm that reduces complexity from quadratic to linear through scalable gradient propagation, enabling high-resolution, long-context Earth modeling. STORM scales to 74,400 GPUs on Frontier with 96--99\% strong-scaling efficiency and up to 6 ExaFLOPs sustained BF16 throughput, while enabling 32,768-member ensembles for uncertainty quantification in 34 seconds on 4,096 GPUs. It scales to 20 billion spatiotemporal tokens and 177,000 temporal frames. Hurricane tracking and long-term climate reanalysis demonstrate improved accuracy, including benefits from longer temporal context and recovery of temperature extremes missed by forecast-only predictions.

cs.LG↗
arXiv2026

A Score Filter Enhanced Data Assimilation Framework for Data-Driven Dynamical Systems

We introduce a score-filter-enhanced data assimilation framework designed to reduce predictive uncertainty in machine learning (ML) models for data-driven dynamical system forecasting. Machine learning serves as an efficient numerical model for predicting dynamical systems. However, even with sufficient data, model uncertainty remains and accumulates over time, causing the long-term performance of ML models to deteriorate. To overcome this difficulty, we integrate data assimilation techniques into the training process to iteratively refine the model predictions by incorporating observational information. Specifically, we apply the Ensemble Score Filter (EnSF), a generative AI-based training-free diffusion model approach, for solving the data assimilation problem in high-dimensional nonlinear complex systems. This leads to a hybrid data assimilation-training framework that combines ML with EnSF to improve long-term predictive performance. We shall demonstrate that EnSF-enhanced ML can effectively reduce predictive uncertainty in ML-based Lorenz-96 system prediction and the Korteweg-De Vries (KdV) equation prediction.

math.DS↗
arXiv2026

Error estimates of a training-free diffusion model for high-dimensional sampling

Score-based diffusion models are a powerful class of generative models, but their practical use often depends on training neural networks to approximate the score function. Training-free diffusion models provide an attractive alternative by exploiting analytically tractable score functions, and have recently enabled supervised learning of efficient end-to-end generative samplers. Despite their empirical success, the training-free diffusion models lack rigorous and numerically verifiable error estimates. In this work, we develop a comprehensive error analysis for a class of training-free diffusion models used to generate labeled data for supervised learning of generative samplers. By exploiting the availability of the exact score function for Gaussian mixture models, our analysis avoids propagating score-function approximation errors through the reverse-time diffusion process and recovers classical convergence rates for ODE discretization schemes, such as first-order convergence for the Euler method. Moreover, the resulting error bounds exhibit favorable dimension dependence, scaling as $O(d)$ in the $\ell_2$ norm and $O(\log d)$ in the $\ell_\infty$ norm. Importantly, the proposed error estimates are fully numerically verifiable with respect to both time-step size and dimensionality, thereby bridging the gap between theoretical analysis and observed numerical behavior.

math.NA↗
arXiv2025

IEnSF: Iterative Ensemble Score Filter for Reducing Error in Posterior Score Estimation in Nonlinear Data Assimilation

The Ensemble Score Filter (EnSF) is a score-based diffusion model approach for solving high-dimensional and nonlinear data assimilation problems. While initial applications of EnSF to the Lorenz-96 model and the quasi-geostrophic system showed potential, the current method employs a heuristic weighted sum to combine the prior and the likelihood score functions. This introduces a structural error into the estimation of the posterior score function in the nonlinear setting. This work addresses this challenge by developing an iterative ensemble score filter (IEnSF) that applies an iterative algorithm as an outer loop around the reverse-time stochastic differential equation solver. When the state dynamics or the observation operator is nonlinear, the iterative algorithm can gradually reduce the posterior score estimation error by improving the accuracy of approximating the conditional expectation of the likelihood score function. The number of iterations required depends on the distance between the prior and posterior distributions. Numerical experiments demonstrate that the IEnSF algorithm substantially reduces the error in posterior score estimation in the nonlinear setting and thus improves the accuracy of tracking high-dimensional dynamical systems.

math.NA↗
arXiv2025

A Score-based Diffusion Model Approach for Adaptive Learning of Stochastic Partial Differential Equation Solutions

We propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governing physics into the score function of a diffusion model using simulation data and incorporate observational information via a likelihood-based correction in a reverse-time stochastic differential equation. This enables adaptive learning through iterative refinement of the solution as new data becomes available. To improve computational efficiency in high-dimensional settings, we introduce the ensemble score filter, a training-free approximation of the score function designed for real-time inference. Numerical experiments on benchmark SPDEs demonstrate the accuracy and robustness of the proposed method under sparse and noisy observations.

stat.CO↗
arXiv2025

Stochastic Operator Network: A Stochastic Maximum Principle Based Approach to Operator Learning

We develop a novel framework for uncertainty quantification in operator learning, the Stochastic Operator Network (SON). SON combines the stochastic optimal control concepts of the Stochastic Neural Network (SNN) with the DeepONet. By formulating the branch net as an SDE and backpropagating through the adjoint BSDE, we replace the gradient of the loss function with the gradient of the Hamiltonian from Stohastic Maximum Principle in the SGD update. This allows SON to learn the uncertainty present in operators through its diffusion parameters. We then demonstrate the effectiveness of SON when replicating several noisy operators in 2D and 3D.

cs.LG↗
arXiv2025

Federated Learning on Stochastic Neural Networks

Federated learning is a machine learning paradigm that leverages edge computing on client devices to optimize models while maintaining user privacy by ensuring that local data remains on the device. However, since all data is collected by clients, federated learning is susceptible to latent noise in local datasets. Factors such as limited measurement capabilities or human errors may introduce inaccuracies in client data. To address this challenge, we propose the use of a stochastic neural network as the local model within the federated learning framework. Stochastic neural networks not only facilitate the estimation of the true underlying states of the data but also enable the quantification of latent noise. We refer to our federated learning approach, which incorporates stochastic neural networks as local models, as Federated stochastic neural networks. We will present numerical experiments demonstrating the performance and effectiveness of our method, particularly in handling non-independent and identically distributed data.

cs.LG↗
arXiv2025

On the sensitivity of different ensemble filters to the type of assimilated observation networks

Recent advances in data assimilation (DA) have focused on developing more flexible approaches that can better accommodate nonlinearities in models and observations. However, it remains unclear how the performance of these advanced methods depends on the observation network characteristics. In this study, we present initial experiments with the surface quasi-geostrophic model, in which we compare a recently developed AI-based ensemble filter with the standard Local Ensemble Transform Kalman Filter (LETKF). Our results show that the analysis solutions respond differently to the number, spatial distribution, and nonlinear fraction of assimilated observations. We also find notable changes in the multiscale characteristics of the analysis errors. Given that standard DA techniques will be eventually replaced by more advanced methods, we hope this study sets the ground for future efforts to reassess the value of Earth observation systems in the context of newly emerging algorithms.

physics.ao-ph↗
arXiv2025

Batch Sample-wise Stochastic Optimal Control via Stochastic Maximum Principle

In this work, we study the stochastic optimal control problem (SOC) mainly from the probabilistic view point, i.e. via the Stochastic Maximum principle (SMP) \cite{Peng4}. We adopt the sample-wise backpropagation scheme proposed in \cite{Hui1} to solve the SOC problem under the strong convexity assumption. Importantly, in the Stochastic Gradient Descent (SGD) procedure, we use batch samples with higher order scheme in the forward SDE to improve the convergence rate in \cite{Hui1} from $\sim \mathcal{O}(\sqrt{\frac{N}{K} + \frac{1}{N}})$ to $\sim \mathcal{O}(\sqrt{\frac{1}{K} + \frac{1}{N^2}})$ and note that the main source of uncertainty originates from the scheme for the simulation of $Z$ term in the BSDE. In the meantime, we note the SGD procedure uses only the necessary condition of the SMP, while the batch simulation of the approximating solution of BSDEs allows one to obtain a more accurate estimate of the control $u$ that minimizes the Hamiltonian. We then propose a damped contraction algorithm to solve the SOC problem whose proof of convergence for a special case is attained under some appropriate assumption. We then show numerical results to check the first order convergence rate of the projection algorithm and analyze the convergence behavior of the damped contraction algorithm. Lastly, we briefly discuss how to incorporate the proposed scheme in solving practical problems especially when the Randomized Neural Networks are used. We note that in this special case, the error backward propagation can be avoided and parameter update can be achieved via purely algebraic computation (vector algebra) which will potentially improve the efficiency of the whole training procedure. Such idea will require further exploration and we will leave it as our future work.

math.OC↗
arXiv2025

Diffusion-based supervised learning of generative models for efficient sampling of multimodal distributions

We propose a hybrid generative model for efficient sampling of high-dimensional, multimodal probability distributions for Bayesian inference. Traditional Monte Carlo methods, such as the Metropolis-Hastings and Langevin Monte Carlo sampling methods, are effective for sampling from single-mode distributions in high-dimensional spaces. However, these methods struggle to produce samples with the correct proportions for each mode in multimodal distributions, especially for distributions with well separated modes. To address the challenges posed by multimodality, we adopt a divide-and-conquer strategy. We start by minimizing the energy function with initial guesses uniformly distributed within the prior domain to identify all the modes of the energy function. Then, we train a classifier to segment the domain corresponding to each mode. After the domain decomposition, we train a diffusion-model-assisted generative model for each identified mode within its support. Once each mode is characterized, we employ bridge sampling to estimate the normalizing constant, allowing us to directly adjust the ratios between the modes. Our numerical examples demonstrate that the proposed framework can effectively handle multimodal distributions with varying mode shapes in up to 100 dimensions. An application to Bayesian inverse problem for partial differential equations is also provided.

stat.ML↗
arXiv2025

Ensemble Score Filter for Data Assimilation of Two-Phase Flow Models in Porous Media

Numerical modeling and simulation of two-phase flow in porous media is challenging due to the uncertainties in key parameters, such as permeability. To address these challenges, we propose a computational framework by utilizing the novel Ensemble Score Filter (EnSF) to enhance the accuracy of state estimation for two-phase flow systems in porous media. The forward simulation of the two-phase flow model is implemented using a mixed finite element method, which ensures accurate approximation of the pressure, the velocity, and the saturation. The EnSF leverages score-based diffusion models to approximate filtering distributions efficiently, avoiding the computational expense of neural network-based methods. By incorporating a closed-form score approximation and an analytical update mechanism, the EnSF overcomes degeneracy issues and handles high-dimensional nonlinear filtering with minimal computational overhead. Numerical experiments demonstrate the capabilities of EnSF in scenarios with uncertain permeability and incomplete observational data.

math.NA↗
arXiv2025

State Estimation Using Particle Filtering in Adaptive Machine Learning Methods: Integrating Q-Learning and NEAT Algorithms with Noisy Radar Measurements

Reliable state estimation is essential for autonomous systems operating in complex, noisy environments. Classical filtering approaches, such as the Kalman filter, can struggle when facing nonlinear dynamics or non-Gaussian noise, and even more flexible particle filters often encounter sample degeneracy or high computational costs in large-scale domains. Meanwhile, adaptive machine learning techniques, including Q-learning and neuroevolutionary algorithms such as NEAT, rely heavily on accurate state feedback to guide learning; when sensor data are imperfect, these methods suffer from degraded convergence and suboptimal performance. In this paper, we propose an integrated framework that unifies particle filtering with Q-learning and NEAT to explicitly address the challenge of noisy measurements. By refining radar-based observations into reliable state estimates, our particle filter drives more stable policy updates (in Q-learning) or controller evolution (in NEAT), allowing both reinforcement learning and neuroevolution to converge faster, achieve higher returns or fitness, and exhibit greater resilience to sensor uncertainty. Experiments on grid-based navigation and a simulated car environment highlight consistent gains in training stability, final performance, and success rates over baselines lacking advanced filtering. Altogether, these findings underscore that accurate state estimation is not merely a preprocessing step, but a vital component capable of substantially enhancing adaptive machine learning in real-world applications plagued by sensor noise.

cs.LG↗