Understanding How Humans Inject Knowledge into Machine Learning Workflows through Visual Analytics

Visual analytics (VA) plays an increasingly important role in supporting machine learning (ML) workflows. In the field of visualization, such approaches and techniques are referred to as VIS4ML. While ML models are mostly learned automatically, the corresponding ML workflows receive a variety of human inputs, such as data labelling, feature engineering, model architecture designing, hyper-parameter tuning, and so on. In this work, we surveyed over 200 VIS4ML papers to gain an understanding of how humans inject their knowledge into ML workflows through interactive visualization. We collected a corpus of VIS4ML papers from the IEEE VIS conferences in the past decade. We developed a coding scheme to facilitate the literature research from four perspectives: characteristics of ML, visualization, interaction, and actions. The analysis of the coded dataset allows us to observe different pathways that transfer human knowledge to ML workflows via interactive visualization. Building on the analysis, we explain the phenomena of VIS4ML using the conceptual model that views VA as model building and the information-theoretic cost-benefit analysis that reasons VA as for optimizing ML workflows. This work provides unequivocal evidence showing the merits of using VA in ML workflows. The full list of surveyed papers, along with all analysis results and figures, is available at https://vis4ml4hd.github.io/ml-knowledge-inject-va/.

Learning Fluid-Structure Interaction Dynamics with Physics-Informed Neural Networks and Immersed Boundary Methods

We introduce neural network architectures that combine physics-informed neural networks (PINNs) with the immersed boundary method (IBM) to solve fluid-structure interaction (FSI) problems. Our approach features two distinct architectures: a Single-FSI network with a unified parameter space, and an innovative Eulerian-Lagrangian network that maintains separate parameter spaces for fluid and structure domains. We study each architecture using standard Tanh and adaptive B-spline activation functions. Empirical studies on a 2D cavity flow problem involving a moving solid structure show that the Eulerian-Lagrangian architecture performs significantly better. The adaptive B-spline activation further enhances accuracy by providing locality-aware representation near boundaries. While our methodology shows promising results in predicting the velocity field, pressure recovery remains challenging due to the absence of explicit force-coupling constraints in the current formulation. Our findings underscore the importance of domain-specific architectural design and adaptive activation functions for modeling FSI problems within the PINN framework.

QCPINN: Quantum Classical Physics-Informed Neural Networks for Solving PDEs

Hybrid quantum-classical neural network methods represent an emerging approach to solving computational challenges by leveraging advantages from both paradigms. As physics-informed neural networks (PINNs) have successfully applied to solve partial differential equations (PDEs) by incorporating physical constraints into neural architectures, this work investigates whether quantum-classical physics-informed neural networks (QCPINNs) can efficiently solve PDEs with reduced parameter counts compared to classical approaches. We evaluate two quantum circuit paradigms: continuous-variable (CV) and qubit-based discrete-variable (DV) across multiple circuit ansatze (Alternate, Cascade, Cross mesh, and Layered). Benchmarking across five challenging PDEs (Helmholtz, Cavity, Wave, Klein-Gordon, and Convection-Diffusion equations) demonstrates that our hybrid approaches achieve comparable accuracy to classical PINNs while requiring up to 89% fewer trainable parameters. DV-based implementations, particularly those with angle encoding and cascade circuit configurations, exhibit better stability and convergence properties across all problem types. For the Convection-Diffusion equation, our angle-cascade QCPINN achieves parameter efficiency and a 37% reduction in relative L2 error compared to classical counterparts. Our findings highlight the potential of quantum-enhanced architectures for physics-informed learning, establishing parameter efficiency as a quantifiable quantum advantage while providing a foundation for future quantum-classical hybrid systems solving complex physical models.