Pruning AMR: Efficient Visualization of Implicit Neural Representations via Weight Matrix Analysis

TL;DR

This paper introduces PruningAMR, an adaptive mesh refinement method guided by weight-matrix pruning to visualize pre-trained implicit neural representations (INRs) without access to training data. By applying interpolative decomposition pruning on INR weight matrices restricted to each mesh element, the algorithm estimates local geometric feature complexity and refines the mesh accordingly, producing high-resolution visualizations with reduced memory footprints. The approach is validated across 2D, 3D, and 4D INRs, including a physics-informed Navier–Stokes PINN and CT-based dynamic INRs, demonstrating substantial DOF (memory) savings while maintaining accuracy. The method offers a practical path for memory-efficient INR visualization in applications like dynamic micro-CT and real-time visualization pipelines.

Abstract

An implicit neural representation (INR) is a neural network that approximates a spatiotemporal function. Many memory-intensive visualization tasks, including modern 4D CT scanning methods, represent data natively as INRs. While INRs are prized for being more memory-efficient than traditional data stored on a lattice, many visualization tasks still require discretization to a regular grid. We present PruningAMR, an algorithm that builds a mesh with resolution adapted to geometric features encoded by the INR. To identify these geometric features, we use an interpolative decomposition pruning method on the weight matrices of the INR. The resulting pruned network is used to guide adaptive mesh refinement, enabling automatic mesh generation tailored to the underlying resolution of the function. Starting from a pre-trained INR--without access to its training data--we produce a variable resolution visualization with substantial memory savings.

Figures (13)

• Figure 1: Graphical depiction of an iteration of the PruningAMR algorithm. The algorithm takes as input an initial mesh, a pre-trained INR, an error tolerance $T$, and a proportion $P \in (0,1)$ of the maximum number of neurons allowed after pruning to end refinement for an element. For each element in the mesh, we sample a random set of points from that element. We then pass these points into the INR and use the output to decide how to prune the INR. After pruning, we record the proportion $p$ of remaining neurons to the original number of neurons and the relative error ($error$) of the pruned INR restricted to that element. We compare these values to $P$ and $T$ to decide whether or not to refine the element. We repeat this procedure until all elements satisfy $p<P$ and $error < T$ or the maximum number of iterations is reached.
• Figure 2: As validation for the approach of Algorithm \ref{['alg:amr4inr']}, we use an INR trained to fit the 2D oscillatory function shown in the upper left. On each element in each of the three meshes shown, we call the prune routine, keeping $\varepsilon$ and $n_{ID}$ fixed, and report the number of neurons at the conclusion of pruning. Notice that more neurons are needed near the origin, where the function has higher oscillation. Also notice that as the elements get smaller with each respective mesh, fewer neurons may be needed per element to describe a given region of the domain. These findings are consistent with the notion that pruning to a smaller neuron count correlates with simpler geometric features present in that region.
• Figure 3: Left: Total error versus number of degrees of freedom plot is shown for Uniform, and the best-tuned instances of BasicAMR ($\tau=0.1$) and PruningAMR ($T=0.1$, $P=0.09$, and $\varepsilon = 10^{-3}$). The PruningAMR method---i.e. Algorithm \ref{['alg:amr4inr']}---drives down error at a faster rate than the Uniform approach and terminates with a lower error for an equivalent number of DOFs than either BasicAMR or Uniform. Right: Table of DOFs and error values for each algorithm at their final iteration.
• Figure 4: We compare three approaches to mesh refinement from a qualitative perspective for the 2D benchmark example. The bottom row shows the mesh at the final state of the refinement method. The top row shows a bilinear interpolant of the INR data evaluated at vertices of the mesh. Treating Uniform as "ground truth," observe that BasicAMR has multiple level sets with inaccurate variations, whereas PruningAMR is visibly more similar to the Uniform image.
• Figure 5: Comparison of 3D visualizations of the Navier--Stokes PINN created by Uniform, BasicAMR ($\tau = 10^{-3}$), and PruningAMR ($T=10^{-3}$, $P=0.15$, $\varepsilon = 0.005$) refinement for fluid flow past a circular cylinder. Note that two dimensions are in space and one is in time. The difference between each visualization appears negligible.