Engineering Material Neural Networks

• Engineering Material Neural Networks (EMNNs) are load-bearing, adaptive structures that embody neural network principles by tuning physical properties such as stiffness and conductivity.
• They integrate mechanical design with learning algorithms, where physical parameters are updated using gradient-descent–inspired techniques to optimize output accuracy.
• A notable implementation, PAMMUNN, demonstrates these concepts through data-aware backpropagation and closed-loop optimization in real-world, hygromorphic composite systems.

Engineering Material Neural Networks (EMNNs) are load-bearing, architected material structures with trainable physical parameters whose overall behavior is adapted to learn a task-relevant mapping. They were formalized as a subcategory of Physical Neural Networks (PNNs) in 2026 and are defined as neuromorphic structures that convert physical variables into measurable outputs by approximating a physical function through their architecture, using the intrinsic properties of a material. In the same period, a physical adaptive material motor unit neural network (PAMMUNN) was presented as a proof of concept: a hygromorph composite machine in which wood–carbon-black actuators, neural-network training, and adaptive shading control are coupled within one materialized system (Kergariou et al., 5 Jun 2026, Kergariou et al., 5 Jun 2026).

1. Definition and formal criteria

The foundational EMNN formulation is motivated by the proposition that networks of interconnected nodes can approximate continuous functions, and that the same principle can be translated into structural matter. In this framework, the adjustable coefficients of an artificial neural network are reinterpreted as physical parameters such as stiffness, conductivity, or magnetic response. The perspective paper gives a thermal example in which the forward map is written as

$T_o=f(\lambda_{ij};T_i),$

with $T_o$ the output temperature, $T_i$ the input temperature(s), and $\lambda_{ij}$ the trainable physical coefficients, interpreted there as thermal conductivity between nodes. The same source then formalizes a learning loop through a loss $L=l(T_o,T_{target})$, a gradient with respect to the physical parameters, and the gradient-descent update

$$\lambda \leftarrow \lambda - \mu \nabla_{\lambda} L.$$

This is presented as a formal analogy for how physical parameters in the material would be updated (Kergariou et al., 5 Jun 2026).

Three defining rules are stated. First, the structure must feature an assembly of individual interconnected material nodes, and each node must be individually adaptable. Second, the output of the system must be adaptable according to the demand of the user. Third, the design should optimize energy efficiency, output accuracy, independence from traditional digital computations, and speed of convergence. The same framework distinguishes several operational terms. “Autonomous actuation” denotes feedforward inference using physically obtained inputs; “feedback control” denotes updating the weight or physical parameter of the network; “learning” denotes optimization of trainable parameters for a specific task; and “adaptation” denotes a change in behavior or response after an adaptation trigger (Kergariou et al., 5 Jun 2026).

A central feature of the definition is that EMNNs are not merely materials that respond to stimuli. They are intended to approximate functions, adapt internal physical parameters, and update behavior in service. Inputs and outputs may be the same physical quantity or different ones, including transduction functions. This makes the EMNN concept broader than a single sensing or actuation mechanism, while keeping the requirement that the computational substrate remains embodied in structural matter (Kergariou et al., 5 Jun 2026).

2. Position within metamaterials, computational matter, and physical neural networks

EMNNs are explicitly distinguished from classical metamaterials. The perspective paper treats metamaterials as architected three-dimensional structures whose emergent response derives from collective meta-atom effects and whose structural parameters are generally fixed after fabrication. EMNNs share the network-like, node-based architecture, but differ in that their material parameters are trainable and adaptable, and their operation includes a training or adaptation phase rather than only a programmed forward response. The distinction is therefore not architectural alone; it lies in the presence of trainability, user-driven output adaptation, and in-service learning (Kergariou et al., 5 Jun 2026).

They are also distinguished from the broader category of “materials that compute.” Prior work on pattern recognition or matrix-vector multiplication in matter is treated as an important precursor, but typically as task-specific and not necessarily adaptive, not necessarily load-bearing, and not necessarily organized as trainable physical networks. Similarly, many PNNs implemented in optics, acoustics, microwaves, or hybrid electronic platforms are not regarded as EMNNs because they rely on external electronics for modulation, memory, control, readout, or training. In the EMNN formulation, computation must be materially embodied in a load-bearing engineering structure whose internal physical properties act as the trainable weights (Kergariou et al., 5 Jun 2026).

This distinction clarifies a common misconception: distributed or embedded intelligence is not by itself sufficient for EMNN status. For example, embedded inference in robotic materials using microcontrollers co-located with sensors and actuators constitutes a practical route toward material intelligence, but it is described as “material-adjacent neural networks” rather than learning directly in the material substrate itself. The open-source nn4mc workflow transfers models trained in TensorFlow/Keras or PyTorch into C code for microcontrollers near sensors and actuators, thereby embedding inference inside smart tires, tactile sensors, and composites; however, the trainable substrate remains the embedded electronics rather than the material architecture itself (Manzano et al., 2019).

The perspective paper therefore ranks training strategies by physical adaptability. Its spectrum runs from in-silico training, through physics-aware training and adjoint-based backpropagation, to direct feedback alignment, extreme learning machine or reservoir computing, zeroth-order gradient estimation, equilibrium propagation or Hebbian adaptation, local learning, Hamiltonian Echo Backpropagation, and finally full physical feedback control. The key claim is that most existing systems remain intermediate cases because learning is still too digital or externally controlled (Kergariou et al., 5 Jun 2026).

3. PAMMUNN: a hygromorph composite realization

The most explicit EMNN realization in the supplied literature is the Physical Adaptive Material Motor Unit Neural Network (PAMMUNN), introduced as a material system that can be organized and trained like a neural network, not just modeled by one. At the material level, PAMMUNN is built from a hygromorphic composite combining wood-based thermoplastic, specifically Laywood meta 5, with carbon black–reinforced PLA. The wood-fiber-dominated phase provides hygromorphic actuation through drying and swelling under environmental humidity changes, while the carbon black PLA acts as the conductive and heating layer. When voltage is applied, Joule heating dries the wood-based fibers and changes the curvature or opening of the actuator. The actuator is therefore sensitive to both temperature and relative humidity, with voltage as the control trigger. In the reported experiments, actuators were tested in a conditioned box with measurable temperature, relative humidity, and light, and the environmental humidity was stabilized after 24 h before recordings (Kergariou et al., 5 Jun 2026).

The architecture is deliberately motor-unit-like. The biological analogy is one motor neuron driving a set of muscle fibers; the engineering implementation uses a central voltage controller driving a small set of identical material actuating “neurons.” The physical geometry is a Quadruple Stacked Down Facing (QSDF) aperture setup comprising four identical actuating blocks arranged in a stacked shading façade. In this analogy, the motor neuron corresponds to voltage control, while the actuator blocks correspond to muscle fibers. Shading output is modulated by varying the voltage inputs to each actuator, analogous to varying motor-unit firing and recruitment in muscle contraction (Kergariou et al., 5 Jun 2026).

The neural-network formalism is intentionally simple. The model is a single-layer neural network with seven nodes and sigmoid activation functions. Its inputs are outside or input light $LX_1$ and $LX_2$, relative humidity $RH$, and temperature $T$; the output is transmitted or internal light $T_o$0 inside the box. Inputs and outputs are scaled to $T_o$1, the data are split into 80% training and 20% validation, and training is stopped after 2000 epochs if validation loss stops improving. The loss is given as

$T_o$2

and the weights are optimized by gradient descent with learning rate $T_o$3 (Kergariou et al., 5 Jun 2026).

A further distinctive feature is the training methodology, termed data-aware back-propagation training. It is distinguished from physics-aware backpropagation by not requiring an explicit digital physics model of the actuator. Instead, experimentally acquired data act as the surrogate. After training, the feedforward model is used to infer actuator voltages required to achieve a target light output. The optimization stage employs SciPy’s optimize(method='L-BFGS-B') to minimize the squared difference between target light and predicted light. The paper then introduces a second-stage refinement in which stabilized $T_o$4 and $T_o$5 are estimated empirically from voltage, reinserted, and optimized again. The reported empirical interpolations are

$T_o$6

and

$T_o$7

This means the controller iteratively corrects itself for the environment it helps create, rather than predicting from static measurements alone (Kergariou et al., 5 Jun 2026).

4. Learning, memory, and closed-loop optimization

PAMMUNN is presented not only as a predictor but as a materialized adaptive system with an expanding database. The database contains more than 300 data points in the main text, while the broader account describes more than 350 experimental data points overall. New runs are appended after each experiment, and this expanding database is central to the claim of incremental learning. In the incremental-learning study, 35 randomly selected points or configurations are used as a fixed evaluation set while the training database size increases progressively. As the number of training examples grows, the standard deviation of prediction error drops sharply up to around 120 database points and stabilizes near $T_o$8 lx, while the correlation coefficient $T_o$9 rises and converges to $T_i$0. At the last validation stage, four out of five predicted values fall within $T_i$1 lx of the target (Kergariou et al., 5 Jun 2026).

The system is also used as an optimizer over multiple actuator configurations. In the reported physical-mode experiments, the model identifies two distinct voltage configurations that produce the same or nearly the same target output under different inputs. The targeted conditions are stated as $T_i$2 lx, $T_i$3, $T_i$4, $T_i$5 for one condition, and $T_i$6 lx, $T_i$7, $T_i$8, $T_i$9 for the second. The optimizer returns the voltage sets $\lambda_{ij}$0 V and $\lambda_{ij}$1 V, with predicted outputs close to the targets: about 181.2 lx for condition 1 and about 183.4 lx for condition 2 in one reporting instance. Physical implementation gives outputs close to the optimized values, with deviations reported on the order of 5.5–13.3 lx depending on configuration (Kergariou et al., 5 Jun 2026).

Two operational scenarios are used to demonstrate adaptive control. In Scenario 1, a target light interval is changed by the user, and the model drives the output from about 239.4 lx to 88.8 lx in under 150 min, for a total correction of 150.6 lx. In Scenario 2, after convergence, the input light changes abruptly and the system re-converges to the same 80–100 lx target band in under 70 min, achieving a 50 lx reduction. These demonstrations are presented as closed-loop optimization: learned mappings choose voltages, physical actuators implement the control, and the resulting measurements are reabsorbed into the database (Kergariou et al., 5 Jun 2026).

Within the EMNN interpretation, the significance of these results is that computation, memory, learning, and actuation are merged within one material architecture. The actuators are not treated merely as outputs of an external controller. Rather, the voltage-actuated composite functions as the neuron-like unit, material properties serve as the computational medium, the database stores experience or memory, backpropagation-like training provides learning, and the opening or closing motion performs the output function. This suggests a shift from “smart material plus controller” toward “material neural network” as an organizing principle (Kergariou et al., 5 Jun 2026).

5. Related EMNN-like research programs

The current EMNN literature is heterogeneous. Much of it does not implement the full 2026 definition, but it supplies the main technical trajectories from which EMNNs are assembled: data-driven processing–structure–property learning (Olesegun et al., 2019), differentiable material–geometry co-optimization (Chandrasekhar et al., 2021), thermodynamically constrained constitutive surrogates (Zhang et al., 2020), hybrid plasticity–damage models (Settgast et al., 2019), physically engineered interaction-field networks (Hu et al., 10 Mar 2026), graph materials models with engineered physical descriptors (Tao et al., 2024), embedded inference in robotic materials (Manzano et al., 2019), spiking constitutive regression (Henkes et al., 2022), and FEM-like neural weak-form solvers (Abda et al., 21 Jan 2025).

Research direction	Representative system	EMNN-relevant mechanism
Processing–structure–property learning	Deep CNNs and generative models for Ti-6Al-4V	Latent feature learning and inverse design
Material–geometry co-optimization	VAE + fully connected networks + FEA	Differentiable material selection
Constitutive law learning	TCNN, HyMNNA	Physics-constrained material surrogates
Physics-engineered materials architectures	mPFDNN, EOSnet	Symmetry-aware, materials-specific representations
Embedded and neuromorphic deployment	nn4mc, SNN regression	Local inference and low-energy constitutive modeling
FEM–NN hybrid solution methods	FENNM	Weak-form neural approximation with flux information

Two themes recur across these strands. First, many systems replace hand-crafted descriptors or purely phenomenological constitutive functions with learned representations grounded in materials structure. For example, deep CNNs were used to classify Ti-6Al-4V micrographs into 19 heat-treat pedigrees with greater than 95% average accuracy on reserve data, while a modified VGG16 coupled microstructure images and scalar stress input to predict high-cycle fatigue behavior for 11 pedigrees. The same work used Glow and cGAN refinement for latent-space material design exploration (Olesegun et al., 2019). In a different vein, a VAE was trained on 92 SolidWorks materials to map discrete material properties $\lambda_{ij}$2 into a continuous 2D latent space, enabling simultaneous optimization of truss geometry and material choice through backpropagation and a differentiable finite-element solver (Chandrasekhar et al., 2021).

Second, several lines of work embed neural networks inside mechanics rather than using them as unconstrained regressors. A Thermodynamic Consistent Neural Network learned traction–separation relations for a silicon/epoxy interface from 236 TSR data points across 10 loading paths while reducing thermodynamic violations to about 5%, compared with 20%–40% without the thermodynamic constraints (Zhang et al., 2020). HyMNNA embedded neural networks into a rate-independent plasticity and damage framework for foam materials, using RVE data from 324 simulations and reporting a speed-up of about 4000× relative to DNS in a plate-with-hole example (Settgast et al., 2019). Spiking neural networks were then extended to nonlinear and history-dependent regression in continuum mechanics, with reported energy reductions of 120× and 238× in the cited hardware comparisons, suggesting a path toward low-power material-model inference (Henkes et al., 2022).

A distinct but related branch engineers network architecture from materials physics itself. mPFDNN integrates Material Property Fields with a Hopfield framework, treating interatomic nonlinear interactions as hidden neurons and using recursive updates to build a deep, analytically tractable DNN for crystals, molecules, and aqueous solutions (Hu et al., 10 Mar 2026). EOSnet embeds Gaussian Overlap Matrix fingerprints into graph node features and reports a band-gap MAE of 0.163 eV and 97.7% accuracy in metal/non-metal classification, emphasizing many-body local environment information rather than manual scalar atom descriptors (Tao et al., 2024). These models are not material neural networks in the structural, load-bearing sense of the 2026 definition; however, they exemplify the broader EMNN ambition to make architecture, representation, and training materials-specific rather than generic.

6. Candidate materials, bottlenecks, and development pathway

The perspective literature identifies four principal candidate material classes for EMNNs: composites, microstructured and micro-architected materials, biological materials, and engineering living materials. Composites are highlighted because multiple phases can combine mechanical and functional responses in a single node, including stiffness, conductivity, magnetism, and actuation. Microstructured materials are attractive because geometry can generate bistability, shape morphing, tunable stiffness, and multi-scale node-like behavior. Biological materials are treated as exemplars of distributed sensing, signaling, memory, and adaptation, while engineering living materials are regarded as especially compelling because cells can function like distributed “neurons,” gene circuits can implement stimulus-to-response transformations, and the material can store history, self-repair, and reconfigure (Kergariou et al., 5 Jun 2026).

A corresponding taxonomy classifies materials by reversibility of adaptation. Non-adaptive materials do not change under a trigger. Non-permanently adaptive materials (NPAMs) change temporarily and return to the original state under a countertrigger. Permanently non-reversible adaptive materials (PNRAMs) change permanently after a trigger and cannot be restored to the initial state. Permanently reversible adaptive materials (PRAMs) change persistently under one trigger but can return via another trigger. PRAMs are treated as ideal candidates for EMNNs because they support repeated reprogramming while maintaining stable state control (Kergariou et al., 5 Jun 2026).

The same literature is explicit about present bottlenecks. Learning is often not physically embedded, since many systems still rely on external computation, manual updates, electronic control, or off-board optimization. Node connectivity and geometry are not yet ideal; many reported structures are linearly arranged or irregularly connected rather than true grid-like node networks. Stable-state multiplicity is limited, with many adaptive materials exhibiting only two stable states. Connector design is difficult because connectors must preserve or exceed the functional contrast of the nodes themselves, such as high thermal conductivity for thermal interconnects or high stiffness for mechanical interconnects. Load-bearing performance must coexist with deformability, and intermediate training hardware can be intrusive (Kergariou et al., 5 Jun 2026).

For this reason, the literature presents a staged development pathway rather than claiming full realization. Material Motor Unit Neural Networks (MMUNNs) are described as a less restrictive precursor in which a centralized control system compares target and actual output and node parameters are optimized digitally. PAMMUNN can be read as such an intermediate embodiment, even though it is also presented as an EMNN proof of concept. A plausible implication is that early EMNN systems will remain hybrid: physical forward inference and materialized actuation will appear first, while fully local physical feedback and weight updates will emerge later.

Three future directions are prioritized. One is the development of permanently reversible adaptive materials. A second is the embedding of training and feedback loops into the material structure, especially via microstructure, biological matter, or living materials. The third is the creation of materials capable of computing, not only for forward inference but also for feedback and weight updates. In that sense, the EMNN program proposes a transition from passive materials to intelligent matter, from predetermined response to trainable behavior, and from external digital control to embedded physical learning (Kergariou et al., 5 Jun 2026).