arXiv subjects

Yucheng Fu

Publications and source records attributed to Yucheng Fu.

18 recordsLinked to original sources

arXiv2026

Revisiting Continuous Noise Sampling for Multi-Party Differential Privacy

Combining secure multi-party computation (MPC) with differential privacy (DP) enables multiple parties to release aggregate statistics without a trusted curator, and the core primitive is the protocol to sample noise from a continuous distribution under finite-precision arithmetic. In this paper, we revisit the continuous noise sampling protocols and present several improvements in both security and efficiency. We start by identifying a vulnerability in widely used sample-and-scale constructions. We demonstrate that the scaling operation in arithmetic circuits confines the noise to a sparse, publicly known set of values, so that an adversary can observe the released noisy queries and decide which dataset produced them. As concrete demonstrations, we instantiate attacks on two systems employing such ``flawed'' sampling protocols: Orchard (OSDI'20) for DP secure aggregation and DP-BREM$^+$ (USENIX Sec'25) for DP federated learning. We report a near-$100\%$ attack success rate on both systems, under any noise scaler $s\geq 2$ used in practice. The leakage we reveal is intrinsic to the scaling operation, and direct repairs either substantially sacrifice utility or add significant precision bits to make the sampling more expensive. To address the security and efficiency issues together, we turn to discrete sampling at the granularity of individual biased bits. We make several optimizations to the sampler and prove its security. Our implementation achieves $4\times \sim 612\times$ speedup over existing secure discrete samplers and orders-of-magnitude speedup over the insecure sample-and-scale paradigm, with negligible utility loss compared to the ideal continuous mechanism.

cs.CR↗

arXiv2026

Approximating two-terminal network reliability

We present a fully polynomial-time randomised approximation scheme (FPRAS) for the two-terminal reliability problem on general graphs, both directed and undirected. We also show that the complementary unreliability question is \BIS-hard. The key idea of the algorithm was discovered by GPT-5.6 Sol Ultra.

cs.DS↗

arXiv2026

On Computing Total Variation Distance Between Mixtures of Product Distributions

We study the problem of approximating the total variation distance between two mixtures of product distributions over an $n$-dimensional discrete domain. Given two mixtures $\mathbb{P}$ and $\mathbb{Q}$ with $k_1$ and $k_2$ product distributions over $[q]^n$, respectively, we give a randomized algorithm that approximates $d_{\mathrm{TV}}\left({\mathbb{P}},{\mathbb{Q}}\right)$ within a multiplicative error of $(1\pm \varepsilon)$ in time $\mathrm{poly}((nq)^{k_1+k_2},1/\varepsilon)$. We also study the special case of mixtures of Boolean subcubes over $\{0,1\}^n$. For this class, we give a deterministic algorithm that exactly computes the total variation distance in time $\mathrm{poly}(n,2^{O(k_1+k_2)})$, and show that exact computation is $\#\mathsf{P}$-hard when $k_1+k_2=\Theta(n)$.

cs.DS↗

arXiv2026

Hard-constrained Physics-informed Neural Networks for Interface Problems

Physics-informed neural networks (PINNs) have emerged as a flexible framework for solving partial differential equations, but their performance on interface problems remains challenging because continuity and flux conditions are typically imposed through soft penalty terms. The standard soft-constraint formulation leads to imperfect interface enforcement and degraded accuracy near interfaces. We introduce two ansatz-based hard-constrained PINN formulations for interface problems that embed the interface physics into the solution representation and thereby decouple interface enforcement from PDE residual minimization. The first, termed the windowing approach, constructs the trial space from compactly supported windowed subnetworks so that interface continuity and flux balance are satisfied by design. The second, called the buffer approach, augments unrestricted subnetworks with auxiliary buffer functions that enforce boundary and interface constraints at discrete points through a lightweight correction. We study these formulations on one- and two-dimensional elliptic interface benchmarks and compare them with soft-constrained baselines. In one-dimensional problems, hard constraints consistently improve interface fidelity and remove the need for loss-weight tuning; the windowing approach attains very high accuracy (as low as $O(10^{-9})$) on simple structured cases, whereas the buffer approach remains accurate ($\sim O(10^{-5})$) across a wider range of source terms and interface configurations. In two dimensions, the buffer formulation is shown to be more robust because it enforces constraints through a discrete buffer correction, as the windowing construction becomes more sensitive to overlap and corner effects and over-constrains the problem. This positions the buffer method as a straightforward and geometrically flexible approach to complex interface problems.

math.NA↗

arXiv2026

ArGEnT: Arbitrary Geometry-encoded Transformer for Operator Learning

Learning solution operators on arbitrary geometries remains a central challenge in scientific machine learning, especially for many-query simulation, physics-informed learning, and evolving geometries requiring accurate, geometry-aware predictions at arbitrary spatial locations. Existing operator-learning methods often rely on structured discretizations, explicit geometry parameterizations, or point-cloud formulations that couple geometric representation with solution-query sampling, limiting flexibility on irregular and non-parameterized domains. We propose the Arbitrary Geometry-encoded Transformer (ArGEnT), a geometry-conditioned attention framework that decouples geometry encoding from query-point evaluation. We develop three variants: self-attention, cross-attention, and hybrid-attention. ArGEnT can be used independently or integrated with neural operators to incorporate non-geometric physical inputs. In the cross-attention variant, geometry is represented by an independently sampled point cloud used to construct keys and values, while arbitrary solution-query points construct queries. This design enables mesh-independent field prediction, reduces sensitivity to query-point distribution, and allows compact geometric representations to condition large-scale solution evaluations. Across benchmarks in fluid dynamics, solid mechanics, and electrochemical systems, ArGEnT consistently improves accuracy and generalization over standard DeepONet, point-cloud-based operator learning, and geometry-aware transformer baselines. In several cases, it reduces prediction errors by more than an order of magnitude while requiring substantially lower training cost than transformer-based baselines. These results demonstrate that decoupled geometry-query attention provides an accurate, scalable, and flexible framework for operator learning on arbitrary geometries.

cs.LG↗

arXiv2025

On approximating the $f$-divergence between two Ising models

The $f$-divergence is a fundamental notion that measures the difference between two distributions. In this paper, we study the problem of approximating the $f$-divergence between two Ising models, which is a generalization of recent work on approximating the TV-distance. Given two Ising models $\nu$ and $\mu$, which are specified by their interaction matrices and external fields, the problem is to approximate the $f$-divergence $D_f(\nu\,\|\,\mu)$ within an arbitrary relative error $\mathrm{e}^{\pm \varepsilon}$. For $\chi^\alpha$-divergence with a constant integer $\alpha$, we establish both algorithmic and hardness results. The algorithm works in a parameter regime that matches the hardness result. Our algorithm can be extended to other $f$-divergences such as $\alpha$-divergence, Kullback-Leibler divergence, R\'enyi divergence, Jensen-Shannon divergence, and squared Hellinger distance.

cs.DS↗

arXiv2024

Benchmarking Secure Sampling Protocols for Differential Privacy

Differential privacy (DP) is widely employed to provide privacy protection for individuals by limiting information leakage from the aggregated data. Two well-known models of DP are the central model and the local model. The former requires a trustworthy server for data aggregation, while the latter requires individuals to add noise, significantly decreasing the utility of aggregated results. Recently, many studies have proposed to achieve DP with Secure Multi-party Computation (MPC) in distributed settings, namely, the distributed model, which has utility comparable to central model while, under specific security assumptions, preventing parties from obtaining others' information. One challenge of realizing DP in distributed model is efficiently sampling noise with MPC. Although many secure sampling methods have been proposed, they have different security assumptions and isolated theoretical analyses. There is a lack of experimental evaluations to measure and compare their performances. We fill this gap by benchmarking existing sampling protocols in MPC and performing comprehensive measurements of their efficiency. First, we present a taxonomy of the underlying techniques of these sampling protocols. Second, we extend widely used distributed noise generation protocols to be resilient against Byzantine attackers. Third, we implement discrete sampling protocols and align their security settings for a fair comparison. We then conduct an extensive evaluation to study their efficiency and utility.

cs.CR↗

arXiv2023

Physics-Guided Continual Learning for Predicting Emerging Aqueous Organic Redox Flow Battery Material Performance

Aqueous organic redox flow batteries (AORFBs) have gained popularity in renewable energy storage due to their low cost, environmental friendliness and scalability. The rapid discovery of aqueous soluble organic (ASO) redox-active materials necessitates efficient machine learning surrogates for predicting battery performance. The physics-guided continual learning (PGCL) method proposed in this study can incrementally learn data from new ASO electrolytes while addressing catastrophic forgetting issues in conventional machine learning. Using a ASO anolyte database with a thousand potential materials generated by a 780 $\text{cm}^2$ interdigitated cell model, PGCL incorporates AORFB physics to optimize the continual learning task formation and training process. This achieves higher efficiency and robustness compared to the non-physics-guided continual learning while retaining previously learned battery material knowledge. The trained PGCL demonstrates its capability in assessing emerging ASO materials within the established parameter space when evaluated with the dihydroxyphenazine isomers.

physics.chem-ph↗

arXiv2023

Investigation of countercurrent flow profile and liquid holdup in random packed column with local CFD data

Liquid holdup and mass transfer area are critical parameters for packed column design and CO2 capture efficiency prediction. In this paper, a framework was established for modeling the liquid-gas countercurrent flow hydrodynamics in a random packed column with pall rings. Besides the column-averaged information, the radial pall ring distribution, velocity, and liquid holdup profiles are obtained to study the entrance effect and the wall influence in the packed column. With local CFD data, the validated packing specific area ap and liquid velocity uL range for liquid holdup correlation is significantly expanded with respect to existing experimental or column-averaged CFD data. The proposed liquid holdup correlation $h_L \propto u_L^{0.44}$ indicates the random packed column falls in a viscous to turbulent transition regime and it covers a Reynolds Number range of [6.7-40.2]. The derived liquid holdup correlation is in good agreement with existing correlations developed using the column-averaged experimental data.

physics.flu-dyn↗

arXiv2023

Physics-informed machine learning of redox flow battery based on a two-dimensional unit cell model

In this paper, we present a physics-informed neural network (PINN) approach for predicting the performance of an all-vanadium redox flow battery, with its physics constraints enforced by a two-dimensional (2D) mathematical model. The 2D model, which includes 6 governing equations and 24 boundary conditions, provides a detailed representation of the electrochemical reactions, mass transport and hydrodynamics occurring inside the redox flow battery. To solve the 2D model with the PINN approach, a composite neural network is employed to approximate species concentration and potentials; the input and output are normalized according to prior knowledge of the battery system; the governing equations and boundary conditions are first scaled to an order of magnitude around 1, and then further balanced with a self-weighting method. Our numerical results show that the PINN is able to predict cell voltage correctly, but the prediction of potentials shows a constant-like shift. To fix the shift, the PINN is enhanced by further constrains derived from the current collector boundary. Finally, we show that the enhanced PINN can be even further improved if a small number of labeled data is available.

cs.LG↗

arXiv2023

A multifidelity approach to continual learning for physical systems

We introduce a novel continual learning method based on multifidelity deep neural networks. This method learns the correlation between the output of previously trained models and the desired output of the model on the current training dataset, limiting catastrophic forgetting. On its own the multifidelity continual learning method shows robust results that limit forgetting across several datasets. Additionally, we show that the multifidelity method can be combined with existing continual learning methods, including replay and memory aware synapses, to further limit catastrophic forgetting. The proposed continual learning method is especially suited for physical problems where the data satisfy the same physical laws on each domain, or for physics-informed neural networks, because in these cases we expect there to be a strong correlation between the output of the previous model and the model on the current training domain.

math.NA↗

arXiv2023

Scientific Computing Algorithms to Learn Enhanced Scalable Surrogates for Mesh Physics

Data-driven modeling approaches can produce fast surrogates to study large-scale physics problems. Among them, graph neural networks (GNNs) that operate on mesh-based data are desirable because they possess inductive biases that promote physical faithfulness, but hardware limitations have precluded their application to large computational domains. We show that it is \textit{possible} to train a class of GNN surrogates on 3D meshes. We scale MeshGraphNets (MGN), a subclass of GNNs for mesh-based physics modeling, via our domain decomposition approach to facilitate training that is mathematically equivalent to training on the whole domain under certain conditions. With this, we were able to train MGN on meshes with \textit{millions} of nodes to generate computational fluid dynamics (CFD) simulations. Furthermore, we show how to enhance MGN via higher-order numerical integration, which can reduce MGN's error and training time. We validated our methods on an accompanying dataset of 3D $\text{CO}_2$-capture CFD simulations on a 3.1M-node mesh. This work presents a practical path to scaling MGN for real-world applications.

cs.LG↗

arXiv2022

Hydrodynamics of countercurrent flows in a structured packed column: effects of initial wetting and dynamic contact angle

Computational countercurrent flow investigation in the structured packed column is a multiscale problem. Multiphase flow studies using volume of fluid (VOF) method in the representative elementary unit (REU) of the packed column can insight into the local hydrodynamics such as interfacial area, film thickness, etc. The interfacial area dictates the mass transfer in absorption process and thereby overall efficiency of column. Impacts of solvent's physical properties, liquid loads and static contact angle (SCA) on the interfacial area were examined earlier. In the present study, the dynamic contact angle (DCA) was used to explore the impact of contact angle hysteresis on the interfacial area. DCA has more pronounced impact on the interfacial area (10%) for aqueous solvent of 0.10M Sodium hydroxide (NaOH). The interfacial area shows undulation and does not achieve the pseudo-steady state. In contrary, the interfacial area gets a net pseudo-steady value for the aqueous solvent having 40% monoethanolamine (MEA) by weight. The wetting hysteresis was also explored via simulations conducted with initially dry and wetted sheets. For 0.10M NaOH aqueous solvent, the initially wetted sheets lead to slightly higher value of the interfacial area (10%) as compared to the initially dry sheets at the same liquid load and DCA. As expected, wetting hysteresis reduces with increasing liquid loads. On the other hand, wetting hysteresis is not significant for 40% MEA aqueous solvent which might be lower surface tension and higher viscosity. Overall, the effect of the dynamic contact angle is not pronounced as compared to those found in a flat surface.

physics.flu-dyn↗

arXiv2022

Enhanced physics-constrained deep neural networks for modeling vanadium redox flow battery

Numerical modeling and simulation have become indispensable tools for advancing a comprehensive understanding of the underlying mechanisms and cost-effective process optimization and control of flow batteries. In this study, we propose an enhanced version of the physics-constrained deep neural network (PCDNN) approach [1] to provide high-accuracy voltage predictions in the vanadium redox flow batteries (VRFBs). The purpose of the PCDNN approach is to enforce the physics-based zero-dimensional (0D) VRFB model in a neural network to assure model generalization for various battery operation conditions. Limited by the simplifications of the 0D model, the PCDNN cannot capture sharp voltage changes in the extreme SOC regions. To improve the accuracy of voltage prediction at extreme ranges, we introduce a second (enhanced) DNN to mitigate the prediction errors carried from the 0D model itself and call the resulting approach enhanced PCDNN (ePCDNN). By comparing the model prediction with experimental data, we demonstrate that the ePCDNN approach can accurately capture the voltage response throughout the charge--discharge cycle, including the tail region of the voltage discharge curve. Compared to the standard PCDNN, the prediction accuracy of the ePCDNN is significantly improved. The loss function for training the ePCDNN is designed to be flexible by adjusting the weights of the physics-constrained DNN and the enhanced DNN. This allows the ePCDNN framework to be transferable to battery systems with variable physical model fidelity.

physics.chem-ph↗

arXiv2021

Latent Space Simulation for Carbon Capture Design Optimization

The CO2 capture efficiency in solvent-based carbon capture systems (CCSs) critically depends on the gas-solvent interfacial area (IA), making maximization of IA a foundational challenge in CCS design. While the IA associated with a particular CCS design can be estimated via a computational fluid dynamics (CFD) simulation, using CFD to derive the IAs associated with numerous CCS designs is prohibitively costly. Fortunately, previous works such as Deep Fluids (DF) (Kim et al., 2019) show that large simulation speedups are achievable by replacing CFD simulators with neural network (NN) surrogates that faithfully mimic the CFD simulation process. This raises the possibility of a fast, accurate replacement for a CFD simulator and therefore efficient approximation of the IAs required by CCS design optimization. Thus, here, we build on the DF approach to develop surrogates that can successfully be applied to our complex carbon-capture CFD simulations. Our optimized DF-style surrogates produce large speedups (4000x) while obtaining IA relative errors as low as 4% on unseen CCS configurations that lie within the range of training configurations. This hints at the promise of NN surrogates for our CCS design optimization problem. Nonetheless, DF has inherent limitations with respect to CCS design (e.g., limited transferability of trained models to new CCS packings). We conclude with ideas to address these challenges.

cs.LG↗

arXiv2018

Intertrochanteric Fracture Visualization and Analysis Using a Map Projection Technique

Understanding intertrochanteric fracture distribution is an important topic in orthopaedics due to its high morbidity and mortality. The intertrochanteric fracture can contain high-dimensional information including complicated 3D fracture lines, which often make it difficult to visualize or to obtain valuable statistics for clinical diagnosis and prognosis applications. This paper proposed a map projection technique to map the high-dimensional information into a 2D parametric space. This method can preserve the 3D proximal femur surface and structure while visualizing the entire fracture line with a single plot/view. Using this method and a standardization technique, a total of 100 patients with different ages and genders are studied based on the original radiographs acquired by CT scan. The comparison shows that the proposed map projection representation is more efficient and rich in information visualization than the conventional heat map technique. Using the proposed method, a fracture probability can be obtained at any location in the 2D parametric space, from which the most probable fracture region can be accurately identified. The study shows that age and gender have significant influences on intertrochanteric fracture frequency and fracture line distribution.

q-bio.QM↗

arXiv2018

BubGAN: Bubble Generative Adversarial Networks for Synthesizing Realistic Bubbly Flow Images

Bubble segmentation and size detection algorithms have been developed in recent years for their high efficiency and accuracy in measuring bubbly two-phase flows. In this work, we proposed an architecture called bubble generative adversarial networks (BubGAN) for the generation of realistic synthetic images which could be further used as training or benchmarking data for the development of advanced image processing algorithms. The BubGAN is trained initially on a labeled bubble dataset consisting of ten thousand images. By learning the distribution of these bubbles, the BubGAN can generate more realistic bubbles compared to the conventional models used in the literature. The trained BubGAN is conditioned on bubble feature parameters and has full control of bubble properties in terms of aspect ratio, rotation angle, circularity and edge ratio. A million bubble dataset is pre-generated using the trained BubGAN. One can then assemble realistic bubbly flow images using this dataset and associated image processing tool. These images contain detailed bubble information, therefore do not require additional manual labeling. This is more useful compared with the conventional GAN which generates images without labeling information. The tool could be used to provide benchmarking and training data for existing image processing algorithms and to guide the future development of bubble detecting algorithms.

cs.CV↗

arXiv2018

A Compact Exponential Scheme for Solving 1D Unsteady Convection-Diffusion Equation with Neumann Boundary Conditions

In this paper, a high-order exponential scheme is developed to solve the 1D unsteady convection-diffusion equation with Neumann boundary conditions. The present method applies fourth-order compact exponential difference scheme in spatial discretization at all interior and boundary points. The Padé approximation is used for the discretization. The resulting scheme obtains fourth-order accuracy in both spatial and temporal discretization. In each iterative loop, the scheme corresponds to a strictly diagonally dominant tridiagonal matrix equation, which can be inverted by simple tridiagonal Gaussian decomposition. The developed scheme is proved numerically unconditionally stable for convection dominated problems. Four typical PDEs with Neumann boundary conditions are provided to verify the accuracy of the proposed scheme. The results are compared with analytical solutions and numerical results calculated by different numerical methods. It shows that the new scheme produces high accuracy solutions for all the test problems and it is more suitable for dealing with convection dominated problems.

physics.flu-dyn↗