PhysMorph-GS: Shape Morphing & Glass Stability

• PhysMorph-GS is a dual-purpose framework that integrates differentiable MPM simulation with 3D Gaussian Splatting for photorealistic, physics-based shape morphing.
• It employs a deformation-aware upsampling bridge with multi-pass optimization to fuse physics and rendering losses for precise inverse design.
• Additionally, it defines quantitative glass stability indices via DSC protocols, correlating with glass-forming ability for both volcanic and industrial materials.

PhysMorph-GS refers to a differentiable shape morphing system that couples material point method (MPM) simulation with 3D Gaussian Splatting (3DGS) rendering, facilitating end-to-end optimization via direct rendering losses, and also designates a suite of glass stability (GS) parameters quantifying the resistance of natural sub-alkaline glasses to reheating-induced crystallization. In computational graphics, PhysMorph-GS addresses the persistent "rendering gap" in physics-based shape morphing pipelines by introducing a differentiable particle-to-Gaussian bridge. In glass science, GS parameters systematize quantitative assessments of glass-forming ability (GFA) for complex natural materials, using rapid differential scanning calorimetry (DSC) protocols. Both usages share a focus on linking physical state evolution (mechanical deformation or thermal transitions) to measurable, optimizable outcomes (rendered images or crystallization resistance) (Song et al., 21 Nov 2025, Iezzi et al., 2018).

1. Differentiable Shape Morphing: Coupling MPM and 3DGS

PhysMorph-GS integrates a differentiable MPM with 3D Gaussian Splatting by employing a deformation-aware upsampling bridge, mapping sparse particle states $(\mathbf{x}_p, \mathbf{F}_p)$ to dense sets of Gaussians $(\boldsymbol\mu_j, \boldsymbol\Sigma_j)$. Each MPM anchor particle is adaptively subdivided according to local deformation magnitude, producing "render particles" placed by stochastic offsets. A two-scale interpolation then computes local deformation gradients for each render particle, which are blended and used to determine the anisotropic covariance of the corresponding Gaussian via polar decomposition—encoding pure stretch and compression without rotation.

The 3DGS representation allows dense, photorealistic rendering, while the differentiable mapping back to MPM anchor states enables pixel-space losses to inform the underlying physics-based shape deformation (Song et al., 21 Nov 2025).

2. Physics–Rendering Joint Optimization and Loss Architecture

Objective function minimization in PhysMorph-GS comprises both physics and rendering terms: $$\mathcal{L}_\text{total} = \underbrace{\mathcal{L}_\text{mass} + w_{\min}\mathcal{L}_\text{min} + \mathcal{L}_\text{physics}}_\text{MPM} + \underbrace{w_\alpha\mathcal{L}_\alpha + w_d\mathcal{L}_d + w_e\mathcal{L}_e + w_s\mathcal{L}_\text{shrink}}_{\mathcal{L}_\text{render}}$$ where

• $\mathcal{L}_\text{mass}$ encourages mass conservation,
• $\mathcal{L}_\alpha$ and $\mathcal{L}_d$ enforce silhouette and depth map correspondence,
• $\mathcal{L}_e$ matches Sobel edge gradients,
• $\mathcal{L}_\text{shrink}$ penalizes excessive interior opacity.

Gradients from rendering losses flow along two distinct computational paths: from pixel-based losses w.r.t. Gaussian covariances back through the stretch-based mapping to deformation gradients, and from Gaussian means back to particle positions. Through the MPM adjoint, these gradients inform updates to per-particle control deformation gradients $\tilde{\mathbf{F}}_p$ (Song et al., 21 Nov 2025).

3. Adjoint MPM Backpropagation and Multi-Pass Optimization

Backward propagation leverages the adjoint MPM algorithm (e.g., as in DiffTaichi), ensuring proper gradient flow through physics steps (particle–grid transfers, force solves, state updates). PhysMorph-GS employs a multi-pass optimization scheme per training episode: an initial pass solves for physics-only gradients ($\mathbf{g}_\text{phys}$), while subsequent passes inject rendering gradients ($\mathbf{g}_\text{render}$). If $$\mathbf{g}_\text{phys} \cdot \mathbf{g}_\text{render} < 0$$, projection via PCGrad ensures constructive gradient fusion. Optimization uses Adam, progressing the control deformation gradients. This training scheme accelerates convergence, improves boundary fidelity, and prevents collapse into physically plausible but visually implausible morphs (Song et al., 21 Nov 2025).

4. Quantitative Evaluation and Model Performance

Experiments on challenging morphing tasks (e.g., sphere-to-heart, sphere-to-pillar) use $32^3$ spatial grids, approximately $10^3$ anchors, and ~1.3 million Gaussians after upsampling. Across 40–50 episodes over 10 time steps each, PhysMorph-GS achieves a 2.5% reduction in Chamfer distance for depth-supervised variants (from 0.0560 to 0.0546) compared to physics-only baselines. Full multi-modal rendering objectives further enhance boundary reconstruction and allow recovery of thin, complex structures, albeit with a moderate increase in Chamfer error but significantly more refined geometry (4.3× more Gaussians). Physics loss is reduced by 96.5% and depth loss by 75.4% through training; temporal stability is maintained due to strict conservation laws at the anchor particle level (Song et al., 21 Nov 2025).

5. Resolution of the Physics-Based Rendering Gap

PhysMorph-GS closes the longstanding rendering gap in physics-based morphing pipelines by providing a fully differentiable map between physical deformation states and rendered images. This bidirectionality supports direct inverse design of morphing trajectories under physical constraints, solely from target image supervision. It enables physically accurate morphing in visual effects, data-driven design in soft robotics, and generative morphologies in computer-aided engineering, with dense rendering that respects conservation principles at all times (Song et al., 21 Nov 2025).

6. Glass Stability Indices in Chemically Complex Sub-Alkaline Glasses

In materials science, PhysMorph-GS also denotes a methodology for quantifying the thermal stability of natural, sub-alkaline glasses through five GS-parameters derived from DSC onsets:

• Turnbull parameter: $K_T = T_g / T_m$
• Hruby parameter: $K_H = (T_x - T_g)/(T_m - T_x)$
• Weisenberg: $K_w = (T_x - T_g)/T_m$
• Lu–Liu: $K_{LL} = T_x/(T_g + T_m)$
• Gu–Fan: $W_2 = (T_g/T_m) - (T_g/(2T_x - T_g))$

Each GS index increases linearly with SiO$_2$ content, reflecting higher crystallization resistance in silica-rich glasses. Empirical linear regressions yield $R^2>0.88$ for all indices across examined glass compositions.

Sample	SiO$_2$ (wt%)	$K_T$	$K_H$	$K_w$
B100	48.02	0.5748	0.7124	0.1769
B40R60	62.73	0.6010	2.0065	0.2663

These indices tightly correlate (inverse-linear, $R^2\sim 0.99$) with independently measured glass-forming ability metrics (critical cooling rate, $R_c$), validating their physical relevance and utility for both volcanic systems and glass-ceramic engineering (Iezzi et al., 2018).

7. Applications in Inverse Design, Volcanology, and Glass-Ceramic Manufacture

PhysMorph-GS, as a pipeline or assessment suite, facilitates:

• Physics-aware, image-supervised morphing for design, simulation, and synthesis in animation, VFX, and robotics;
• Predictive modeling of devitrification processes in volcanic materials, leveraging GS-parameter variations with bulk chemistry to forecast textural transformation during reheating;
• Efficient screening and design of glass-ceramics using in-situ DSC and GS indices to tailor crystalline phase development for mechanically and functionally optimized products, informed by direct correlations with GFA.

A plausible implication is that PhysMorph-GS frameworks—whether in differentiable shape morphing or glass stability measurement—enable rapid, direct optimization of physical state trajectories against rigorous, domain-specific objectives, reducing the need for ad hoc or indirect heuristic guidance (Song et al., 21 Nov 2025, Iezzi et al., 2018).