arXiv subjects

Keke Wu

Publications and source records attributed to Keke Wu.

At least 19 recordsLinked to original sources

arXiv2026

Bringing Data to Life: Designing Data Characters for the Emotional Self

Journaling is a common practice for emotional expression, reflection, and processing. However, as entries accumulate, it can become difficult to interpret and compare their affective content, especially since traditional text-based analyses and visualizations often struggle to convey affective nuance. We introduce Data Characters, a visualization approach that represents affective content in journaling through human-like characters. Using a customizable Data Character as a design probe, we investigate the potential of character-based representations for conveying affective experiences and explore what visual encodings emerge through customization. Preliminary walkthroughs with two participants demonstrate the intuitiveness and feasibility of the approach. This work contributes an exploratory approach to studying how affective experiences can be visually represented and encoded through anthropomorphic forms.

cs.HC↗

arXiv2026

What Cognitive Accessibility Reveals About Data Visualization

Data visualization aims to augment human cognition and make data accessible to diverse audiences. As data increasingly shapes participation and decision-making across many domains, there is a growing need to examine whether prevailing assumptions in visualization adequately reflect the diversity of human abilities, experiences, and needs. We argue that cognitive accessibility provides a critical lens for examining these questions and functions as a stress test for visualization theory. Drawing on cognitive accessibility research and our experiences studying accessible visualization, we identify three interconnected assumptions that shape visualization research and practice: assumptions about what forms of cognition visualization supports, how accessibility is defined and measured, and whose needs and abilities are centered in design and evaluation. Making these assumptions explicit reveals opportunities to rethink longstanding approaches and open new directions. Ultimately, we believe that cognitive accessibility can serve as a catalyst for innovation, expanding what visualization supports, whom it serves, and the roles it plays in people's lives.

cs.HC↗

arXiv2026

Made to Feel: How Designers Bring Emotions into Affective Visualization

Affective visualization is increasingly studied in visualization research, yet how designers bring emotions into their visualization work remains unexplored. This paper addresses this gap through semi-structured interviews with 15 visualization practitioners. Using hybrid thematic analysis, we identify: (1) three functions that emotions can serve for viewers (entry, engagement, outcome); (2) three facets of how designers work with emotion (data, design, audience), along with design strategies; and (3) ethical considerations in the design process. We also observe that affective intent often emerges during the design process rather than being planned from the outset, and that emotional impact arises from accumulated design choices rather than isolated visual elements. Finally, we highlight evaluation as a key challenge identified by our participants.

cs.HC↗

arXiv2026

Let There Be Light: Reflection, Refraction and Scattering for Neural Operators

Neural operators learn mappings between infinite-dimensional function spaces and provide a data-driven surrogate modeling paradigm for parametric partial differential equations (PDEs). Existing architectures typically obtain expressivity by parameterizing integral kernels in prescribed transform domains or by applying attention-like interactions over discretized spatial points. While these approaches have achieved substantial progress, they often face a persistent trade-off among physical interpretability, nonlocal spatial communication, mesh scalability, and computational cost. We propose a Light-inspired neural operator(LiNO), an operator-learning architecture whose latent evolution is decomposed into three mechanisms motivated by elementary light transport: reflection, refraction, and scattering. Reflection and refraction act as adaptive pointwise transformations in latent feature space, enabling local feature reorientation and anisotropic modulation, whereas scattering performs input-dependent nonlocal propagation over the physical domain. We first formulate scattering as a normalized pairwise kernel with relative positional bias, and then develop an efficient scattering variant that replaces explicit pairwise interactions with positive-feature global propagation and a local diffusion branch, reducing the dominant spatial complexity from quadratic to linear. This yields a structured neural operator that separates local feature modulation from global spatial communication while retaining a modular and interpretable latent evolution.

cs.LG↗

arXiv2026

Asymptotic-Preserving Neural Networks based on Even-odd Decomposition for Multiscale Gray Radiative Transfer Equations

We present a novel Asymptotic-Preserving Neural Network (APNN) approach utilizing even-odd decomposition to tackle the nonlinear gray radiative transfer equations (GRTEs). Our AP loss demonstrates consistent stability concerning the small Knudsen number, ensuring the neural network solution uniformly converges to the diffusion limit solution. This APNN method alleviates the rigorous conservation requirements while simultaneously incorporating an auxiliary deep neural network, distinguishing it from the APNN method based on micro-macro decomposition for GRTE. Several numerical problems are examined to demonstrate the effectiveness of our proposed APNN technique.

math.NA↗

arXiv2025

Uniformly accurate structure-preserving neural surrogates for radiative transfer

In this work, we propose a uniformly accurate, structure-preserving neural surrogate for the radiative transfer equation with periodic boundary conditions based on a multiscale parity decomposition framework. The formulation introduces a refined decomposition of the particle distribution into macroscopic, odd, and higher-order even components, leading to an asymptotic-preserving neural network system that remains stable and accurate across all parameter regimes. By constructing key higher-order correction functions, we establish rigorous uniform error estimates with respect to the scale parameter $\varepsilon$, which ensures $\varepsilon$-independent accuracy. Furthermore, the neural architecture is designed to preserve intrinsic physical structures such as parity symmetry, conservation, and positivity through dedicated architectural constraints. The framework extends naturally from one to two dimensions and provides a theoretical foundation for uniformly accurate neural solvers of multiscale kinetic equations. Numerical experiments confirm the effectiveness of our approach.

math.NA↗

arXiv2025

A Hybrid Discontinuous Galerkin Neural Network Method for Solving Hyperbolic Conservation Laws with Temporal Progressive Learning

For hyperbolic conservation laws, traditional methods and physics-informed neural networks (PINNs) often encounter difficulties in capturing sharp discontinuities and maintaining temporal consistency. To address these challenges, we introduce a hybrid computational framework by coupling discontinuous Galerkin (DG) discretizations with a temporally progressive neural network architecture. Our method incorporates a structure-preserving weak-form loss -- combining DG residuals and Rankine-Hugoniot jump conditions -- with a causality-respecting progressive training strategy. The proposed framework trains neural networks sequentially across temporally decomposed subintervals, leveraging pseudo-label supervision to ensure temporal coherence and solution continuity. This approach mitigates error accumulation and enhances the model's capacity to resolve shock waves and steep gradients without explicit limiters. Besides, a theoretical analysis establishes error bounds for the proposed framework, demonstrating convergence toward the physical solution under mesh refinement and regularized training. Numerical experiments on Burgers and Euler equations show that our method consistently outperforms standard PINNs, PINNs-WE, and first-order DG schemes in both accuracy and robustness, particularly in capturing shocks and steep gradients. These results highlight the promise of combining classical discretization techniques with machine learning to develop robust and accurate solvers for nonlinear hyperbolic systems.

math.NA↗

arXiv2025

A Micro-Macro Decomposition-Based Asymptotic-Preserving Random Feature Method for Multiscale Radiative Transfer Equations

This paper introduces the Asymptotic-Preserving Random Feature Method (APRFM) for the efficient resolution of multiscale radiative transfer equations. The APRFM effectively addresses the challenges posed by stiffness and multiscale characteristics inherent in radiative transfer equations through the application of a micro-macro decomposition strategy. This approach decomposes the distribution function into equilibrium and non-equilibrium components, allowing for the approximation of both parts through the random feature method (RFM) within a least squares minimization framework. The proposed method exhibits remarkable robustness across different scales and achieves high accuracy with fewer degrees of freedom and collocation points than the vanilla RFM. Additionally, compared to the deep neural network-based method, our approach offers significant advantages in terms of parameter efficiency and computational speed. These benefits have been substantiated through numerous numerical experiments conducted on both one- and two-dimensional problems.

math.NA↗

arXiv2024

Our Stories, Our Data: Co-designing Visualizations with People with Intellectual and Developmental Disabilities

Individuals with Intellectual and Developmental Disabilities (IDD) have unique needs and challenges when working with data. While visualization aims to make data more accessible to a broad audience, our understanding of how to design cognitively accessible visualizations remains limited. In this study, we engaged 20 participants with IDD as co-designers to explore how they approach and visualize data. Our preliminary investigation paired four participants as data pen-pals in a six-week online asynchronous participatory design workshop. In response to the observed conceptual, technological, and emotional struggles with data, we subsequently organized a two-day in-person co-design workshop with 16 participants to further understand relevant visualization authoring and sensemaking strategies. Reflecting on how participants engaged with and represented data, we propose two strategies for cognitively accessible data visualizations: transforming numbers into narratives and blending data design with everyday aesthetics. Our findings emphasize the importance of involving individuals with IDD in the design process, demonstrating their capacity for data analysis and expression, and underscoring the need for a narrative and tangible approach to accessible data visualization.

cs.HC↗

arXiv2023

Asymptotic-Preserving Neural Networks for Multiscale Kinetic Equations

In this paper, we present two novel Asymptotic-Preserving Neural Networks (APNNs) for tackling multiscale time-dependent kinetic problems, encompassing the linear transport equation and Bhatnagar-Gross-Krook (BGK) equation with diffusive scaling. Our primary objective is to devise efficient and accurate APNN approaches for resolving multiscale kinetic equations. We have established a neural network based on even-odd decomposition and concluded that enforcing the initial condition for the linear transport equation with inflow boundary conditions is crucial. This APNN method based on even-odd parity relaxes the stringent conservation prerequisites while concurrently introducing an auxiliary deep neural network. Additionally, we have incorporated the conservation laws of mass, momentum, and energy for the Boltzmann-BGK equation into the APNN framework by enforcing exact boundary conditions. This is our second contribution. The most notable finding of this study is that approximating the zeroth, first and second moments of the particle density distribution is simpler than the distribution itself. Furthermore, a compelling phenomenon in the training process is that the convergence of density is swifter than that of momentum and energy. Finally, we investigate several benchmark problems to demonstrate the efficacy of our proposed APNN methods.

math.NA↗

arXiv2023

An Unsupervised Deep Learning Approach for the Wave Equation Inverse Problem

Full-waveform inversion (FWI) is a powerful geophysical imaging technique that infers high-resolution subsurface physical parameters by solving a non-convex optimization problem. However, due to limitations in observation, e.g., limited shots or receivers, and random noise, conventional inversion methods are confronted with numerous challenges, such as the local-minimum problem. In recent years, a substantial body of work has demonstrated that the integration of deep neural networks and partial differential equations for solving full-waveform inversion problems has shown promising performance. In this work, drawing inspiration from the expressive capacity of neural networks, we provide an unsupervised learning approach aimed at accurately reconstructing subsurface physical velocity parameters. This method is founded on a re-parametrization technique for Bayesian inference, achieved through a deep neural network with random weights. Notably, our proposed approach does not hinge upon the requirement of the labeled training dataset, rendering it exceedingly versatile and adaptable to diverse subsurface models. Extensive experiments show that the proposed approach performs noticeably better than existing conventional inversion methods.

math.NA↗

arXiv2023

Capturing the Diffusive Behavior of the Multiscale Linear Transport Equations by Asymptotic-Preserving Convolutional DeepONets

In this paper, we introduce two types of novel Asymptotic-Preserving Convolutional Deep Operator Networks (APCONs) designed to address the multiscale time-dependent linear transport problem. We observe that the vanilla physics-informed DeepONets with modified MLP may exhibit instability in maintaining the desired limiting macroscopic behavior. Therefore, this necessitates the utilization of an asymptotic-preserving loss function. Drawing inspiration from the heat kernel in the diffusion equation, we propose a new architecture called Convolutional Deep Operator Networks, which employ multiple local convolution operations instead of a global heat kernel, along with pooling and activation operations in each filter layer. Our APCON methods possess a parameter count that is independent of the grid size and are capable of capturing the diffusive behavior of the linear transport problem. Finally, we validate the effectiveness of our methods through several numerical examples.

cs.LG↗

arXiv2023

Empowering People with Intellectual and Developmental Disabilities through Cognitively Accessible Visualizations

Data has transformative potential to empower people with Intellectual and Developmental Disabilities (IDD). However, conventional data visualizations often rely on complex cognitive processes, and existing approaches for day-to-day analysis scenarios fail to consider neurodivergent capabilities, creating barriers for people with IDD to access data and leading to even further marginalization. We argue that visualizations could be an equalizer for people with IDD to participate in data-driven conversations. Drawing on preliminary research findings and our experiences working with people with IDD and their data, we introduce and expand on the concept of cognitively accessible visualizations, unpack its meaning and roles in increasing IDD individuals' access to data, and discuss two immediate research objectives. Specifically, we argue that cognitively accessible visualizations should support people with IDD in personal data storytelling for effective self-advocacy and self-expression, and balance novelty and familiarity in data design to accommodate cognitive diversity and promote inclusivity.

cs.HC↗

arXiv2023

Roughness Index for Loss Landscapes of Neural Network Models of Partial Differential Equations

Loss landscape is a useful tool to characterize and compare neural network models. The main challenge for analysis of loss landscape for the deep neural networks is that they are generally highly non-convex in very high dimensional space. In this paper, we develop "the roughness"concept for understanding such landscapes in high dimensions and apply this technique to study two neural network models arising from solving differential equations. Our main innovation is the proposal of a well-defined and easy-to-compute roughness index (RI) which is based on the mean and variance of the (normalized) total variation for one-dimensional functions projected on randomly sampled directions. A large RI at the local minimizer hints an oscillatory landscape profile and indicates a severe challenge for the first-order optimization method. Particularly, we observe the increasing-then-decreasing pattern for RI along the gradient descent path in most models. We apply our method to two types of loss functions used to solve partial differential equations (PDEs) when the solution of PDE is parametrized by neural networks. Our empirical results on these PDE problems reveal important and consistent observations that the landscapes from the deep Galerkin method around its local minimizers are less rough than the deep Ritz method.

math.NA↗

arXiv2023

Data, Data, Everywhere: Uncovering Everyday Data Experiences for People with Intellectual and Developmental Disabilities

Data is everywhere but may not be accessible to everyone. Conventional data visualization tools and guidelines often do not actively consider the specific needs and abilities of people with Intellectual and Developmental Disabilities (IDD), leaving them excluded from data-driven activities and vulnerable to ethical issues. To understand the needs and challenges people with IDD have with data, we conducted 15 semi-structured interviews with individuals with IDD and their caregivers. Our algorithmic interview approach situated data in the lived experiences of people with IDD to uncover otherwise hidden data encounters in their everyday life. Drawing on findings and observations, we characterize how they conceptualize data, when and where they use data, and what barriers exist when they interact with data. We use our results as a lens to reimagine the role of visualization in data accessibility and establish a critical near-term research agenda for cognitively accessible visualization.

cs.HC↗

arXiv2022

Asymptotic-Preserving Neural Networks for Multiscale Time-Dependent Linear Transport Equations

In this paper we develop a neural network for the numerical simulation of time-dependent linear transport equations with diffusive scaling and uncertainties. The goal of the network is to resolve the computational challenges of curse-of-dimensionality and multiple scales of the problem. We first show that a standard Physics-Informed Neural Network (PINN) fails to capture the multiscale nature of the problem, hence justifies the need to use Asymptotic-Preserving Neural Networks (APNNs). We show that not all classical AP formulations are fit for the neural network approach. We construct a micro-macro decomposition based neural network, and also build in a mass conservation mechanism into the loss function, in order to capture the dynamic and multiscale nature of the solutions. Numerical examples are used to demonstrate the effectiveness of this APNNs.

math.NA↗

arXiv2020

Enforcing exact boundary and initial conditions in the deep mixed residual method

In theory, boundary and initial conditions are important for the wellposedness of partial differential equations (PDEs). Numerically, these conditions can be enforced exactly in classical numerical methods, such as finite difference method and finite element method. Recent years have witnessed growing interests in solving PDEs by deep neural networks (DNNs), especially in the high-dimensional case. However, in the generic situation, a careful literature review shows that boundary conditions cannot be enforced exactly for DNNs, which inevitably leads to a modeling error. In this work, based on the recently developed deep mixed residual method (MIM), we demonstrate how to make DNNs satisfy boundary and initial conditions automatically in a systematic manner. As a consequence, the loss function in MIM is free of the penalty term and does not have any modeling error. Using numerous examples, including Dirichlet, Neumann, mixed, Robin, and periodic boundary conditions for elliptic equations, and initial conditions for parabolic and hyperbolic equations, we show that enforcing exact boundary and initial conditions not only provides a better approximate solution but also facilitates the training process.

math.NA↗

arXiv2020

A comparison study of deep Galerkin method and deep Ritz method for elliptic problems with different boundary conditions

Recent years have witnessed growing interests in solving partial differential equations by deep neural networks, especially in the high-dimensional case. Unlike classical numerical methods, such as finite difference method and finite element method, the enforcement of boundary conditions in deep neural networks is highly nontrivial. One general strategy is to use the penalty method. In the work, we conduct a comparison study for elliptic problems with four different boundary conditions, i.e., Dirichlet, Neumann, Robin, and periodic boundary conditions, using two representative methods: deep Galerkin method and deep Ritz method. In the former, the PDE residual is minimized in the least-squares sense while the corresponding variational problem is minimized in the latter. Therefore, it is reasonably expected that deep Galerkin method works better for smooth solutions while deep Ritz method works better for low-regularity solutions. However, by a number of examples, we observe that deep Ritz method can outperform deep Galerkin method with a clear dependence of dimensionality even for smooth solutions and deep Galerkin method can also outperform deep Ritz method for low-regularity solutions. Besides, in some cases, when the boundary condition can be implemented in an exact manner, we find that such a strategy not only provides a better approximate solution but also facilitates the training process.

math.NA↗