Information Propagation and Encoding in Solids: A Quantitative Approach Towards Mechanical Intelligence

TL;DR

The paper develops a quantitative, task-agnostic information-theoretic framework to analyze how information about applied loads propagates through elastic solids, treating the solid as an information encoder and sensor readings as outputs. It defines mutual information and a normalized metric NMI = I(X;Y)/h(X), constructs a load space via Legendre expansions, and uses rate-distortion theory to connect information throughput to reconstruction fidelity, validated on an elastic halfspace and extended to architected materials. Key findings show that information propagation adheres to Saint-Venant’s principle for statically equivalent loads, that greedy sensor placement can reach maximal MI with k = d_x sensors, and that domain geometry (pores vs slits) can substantially tune information flow, which can be further optimized via Bayesian methods. The work provides benchmark tasks and design guidelines for mechanically embodied information processing and outlines future directions toward integrating sensing with memory and actuation in a unified information-theoretic framework.

Abstract

Engineered systems typically separate mechanical function from information processing, whereas biological systems can exploit physical structure as a medium for information processing and computation. Motivated by this contrast, recent work in mechanics has explored embedding information-processing capabilities directly into mechanical structures. However, quantitative frameworks for evaluating such capabilities remain limited. Here we address a foundational question: how does information propagate through a solid body? Using elastic bodies as a model system, we apply information-theoretic tools to treat an elastic domain as an information encoder and quantify how information transmits from applied loads to discrete sensor locations. We further connect these measures to familiar mechanical phenomena, including Saint-Venant's effect and principal stress lines. Moving toward design, we show how geometry and architected materials can tune transmission, enabling elastic domains to either transmit or block information. Overall, this work advances quantifiable metrics and benchmark tasks for mechanical intelligence, supporting comparable designs of mechanically embodied information processing.

Figures (9)

• Figure 1: Interpretation of a mechanical system as an information channel. a) Block diagram of a simple information channel. Input signal $\bm{X} \sim \mathcal{X}$ is compressed to signal $\bm{Y} \sim \mathcal{Y}$ through an encoder. $\bm{Y}$ is then transmitted and passed through a decoder to obtain the final decoded signal $\hat{\bm{X}} \sim \hat{\mathcal{X}}$. b) Schematic of an elastic solid as an information encoder. The load $\bm{X} \sim \mathcal{X}$ is the input signal and the elastic solid body acts as an encoder. The reaction forces measured at discrete sensor points are the output compressed signal $\bm{Y} \sim \mathcal{Y}$.
• Figure 2: Elastic halfspace as an information encoder. a) Schematic of our pipeline to compute mutual information $I(\bm{X};\bm{Y})$ from input loads $\bm{X}$ and measured pointwise internal forces $\bm{Y}$. b) Visualizes pointwise changes of mutual information gain in the elastic halfspace subjected to $X\sim\mathcal{X}_{even}$ loads when sensors are sequentially greedily selected for $d_x = 3$ and $d_x = 6$. Note that $y/a$ is in log-scale but $x/a$ is in linear-scale. c) Visualizes changes of mutual information gain in the elastic halfspace subjected to $X\sim\mathcal{X}_{full}$ loads when sensors are sequentially greedily selected for $d_x = 3$ and $d_x = 6$. Note that $y/a$ is in log-scale but $x/a$ is in linear-scale.
• Figure 3: Elastic halfspace as an information encoder for a full information channel for $\mathcal{X}_{even}$ loads with $4$ Legendre coefficients ($d_x=4$). a) Rate-distortion curve of different number of sensors with different sensor selection schemes. The dotted line is represents the Shannon Lower Bound which is the theoretical lower bound of the optimal performance for a information channel. Insets show representative reconstructed load compared with ground truth for information channels with greedy sensor selection. b) Plot of raw data comparing the load reconstruction error (MSE) for different number of sensors with different sensor selection schemes.
• Figure 4: Effect of domain geometry on information transmission. The left panel visualizes a schematic of the geometries investigated here. Each dotted box contains one unit of the geometry class. Right panel plots the change of normalized mutual information $I(X;Y)/H(X)$ by changing the number of units for both the geometry classes. Insets show the geometry with principal stress lines traced to visualize information flow.
• Figure 5: Bayesian optimization to maximize and minimize information transmission. a) Left panel visualizes design space parameterization for Bayesian optimization. Each individual $i^{th}$ ellipse is parameterized by $a_i$ and $b_i$. Right panel visualizes results from the Bayesian optimization. The black line shows the convergence plot during the maximization process, while the gray line shows the convergence plot during the minimization process. Insets visualizes the principal stress lines of the structure at different points in during the optimization process.