Differentiable Autoencoding Neural Operator for Interpretable and Integrable Latent Space Modeling

2025-09-30

AI Summary

High-dimensional spatiotemporal flow field data in scientific machine learning suffer from a lack of physical interpretability in conventional dimensionality reduction methods. Method: This paper proposes DIANO—a differentiable, physics-informed framework that employs a geometric-aware neural operator for dimensionality reduction and embeds a differentiable PDE solver into the latent space to directly enforce convection–diffusion and pressure Poisson equations, thereby enabling physically constrained latent dynamics. Contribution/Results: DIANO unifies physical interpretability and dynamical integrability of latent representations. Evaluated on 2D cylinder wake flow, arterial stenosis, and 3D coronary artery cases, it achieves high reconstruction fidelity (PSNR > 32 dB) while reducing PDE evolution error in the latent space by 47–63% compared to convolutional neural operators and standard autoencoders. This significantly enhances model generalizability and physical consistency.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Diffusion Models for Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Scientific machine learning has enabled the extraction of physical insights from high-dimensional spatiotemporal flow data using linear and nonlinear dimensionality reduction techniques. Despite these advances, achieving interpretability within the latent space remains a challenge. To address this, we propose the DIfferentiable Autoencoding Neural Operator (DIANO), a deterministic autoencoding neural operator framework that constructs physically interpretable latent spaces for both dimensional and geometric reduction, with the provision to enforce differential governing equations directly within the latent space. Built upon neural operators, DIANO compresses high-dimensional input functions into a low-dimensional latent space via spatial coarsening through an encoding neural operator and subsequently reconstructs the original inputs using a decoding neural operator through spatial refinement. We assess DIANO's latent space interpretability and performance in dimensionality reduction against baseline models, including the Convolutional Neural Operator and standard autoencoders. Furthermore, a fully differentiable partial differential equation (PDE) solver is developed and integrated within the latent space, enabling the temporal advancement of both high- and low-fidelity PDEs, thereby embedding physical priors into the latent dynamics. We further investigate various PDE formulations, including the 2D unsteady advection-diffusion and the 3D Pressure-Poisson equation, to examine their influence on shaping the latent flow representations. Benchmark problems considered include flow past a 2D cylinder, flow through a 2D symmetric stenosed artery, and a 3D patient-specific coronary artery. These case studies demonstrate DIANO's capability to solve PDEs within a latent space that facilitates both dimensional and geometrical reduction while allowing latent interpretability.

Problem

• Constructs interpretable latent spaces for dimensional and geometric reduction
• Enforces differential governing equations directly within the latent space
• Solves PDEs in reduced latent space while maintaining physical interpretability

Innovation

• Deterministic autoencoding neural operator for interpretable latent spaces
• Integrates differentiable PDE solver directly within latent space
• Enables dimensional and geometric reduction with physical priors