Engineering shape optimization faces challenges in both expert-dependent problem setup and surrogate-model reliability. In practical aerodynamic design, optimization settings such as editable regions, deformation ranges, and design-preservation constraints are typically specified manually by experienced engineers, while surrogate-based optimization may become unreliable for heterogeneous geometry databases and out-of-distribution designs. To address these challenges, we propose a knowledge-constrained shape-optimization framework that translates knowledge-based constraints and user intent into quantifiable parameters of DFFD-based deformation operators, enabling engineering-aware and controllable constrained optimization. We further develop a Mixture-of-Experts Neural Operator (MoE-NO) to improve drag prediction and trend consistency over heterogeneous aerodynamic datasets. Based on the MoE-NO encoder and Mahalanobis distance, an uncertainty-estimation strategy is introduced to detect out-of-distribution geometries and selectively trigger physics-solver feedback for local sample enrichment. Experiments on in-house MPV, SUV, and Sedan datasets show that MoE-NO achieves a test-set MAPE of $1.16\%$ and a trend-prediction accuracy of $94.34\%$, outperforming the best baseline results of $1.52\%$ and $90.34\%$, respectively. Vehicle shape-optimization experiments further yield CFD-validated drag coefficient reductions of approximately $4\%$ to $10\%$.
Mirror Illusion Art is a novel reflection-conditioned 3D illusion where one object yields two target appearances (front and mirror). The task is formulated as inverse design from two target 2D images (front and mirror) to a printable 3D object with geometry and texture. Prior topology-driven and shadow-based approaches demand substantial manual effort, optimize shape only, and often yield non-smooth or incomplete geometry. To address these challenges, we propose AutoMIA, an automated Mirror Illusion Art design pipeline that jointly optimizes shape and color. To stabilize optimization and suppress artifacts, four mechanisms are introduced: (1) projection-alignment component (PAC) selection to reduce surface noise, (2) position-weighted adaptive (PWA) suppression for background noise, (3) internal voxel preservation (IVP) to prevent internal fractures, and (4) shape-color decoupled (SCD) optimization that balance shape and color optimization. AutoMIA generate diverse smooth Mirror Illusion artworks successfully both in the digital and physical world, with only around 76s design time and 2.6 GB memory on average using a single RTX 3090, advancing inverse graphics and computational design. Our code is available at https://github.com/zxp555/AutoMIA.
Geometry is central to PDE-governed systems, motivating shape optimization and inversion. Classical pipelines conduct costly forward simulation with geometry processing, requiring substantial expert effort. Neural surrogates accelerate forward analysis but do not close the loop because gradients from objectives to geometry are often unavailable. Existing differentiable methods either rely on restrictive parameterizations or unstable latent optimization driven by scalar objectives, limiting interpretability and part-wise control. To address these challenges, we propose Geometry-Aware Neural Optimizer (GANO), an end-to-end differentiable framework that unifies geometry representation, field-level prediction, and automated optimization/inversion in a single latent-space loop. GANO encodes shapes with an auto-decoder and stabilizes latent updates via a denoising mechanism, and a geometry-injected surrogate provides a reliable gradient pathway for geometry updates. Moreover, GANO supports part-wise control through null-space projection and uses remeshing-free projection to accelerate geometry processing. We further prove that denoising induces an implicit Jacobian regularization that reduces decoder sensitivity, yielding controlled deformations. Experiments on three benchmarks spanning 2D Helmholtz, 2D airfoil, and 3D vehicles show state-of-the-art accuracy and stable, controllable updates, achieving up to +55.9% lift-to-drag improvement for airfoils and ~7% drag reduction for vehicles.