Microstructure-Conditioned Surrogate Models for Graded Multiscale Optimization of Mycelium Composites

arXiv:2607.13688 · cs.LG, cond-mat.mtrl-sci, cs.NA, math.NA, physics.comp-ph · Submitted 2026-07-15 · Read on arXiv

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Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: Hi, I'm Tom.

Jane: And I'm Jane, here with Lu, Meng and our in-house large language model, Lalam.

Tom: We're looking at the paper: "Microstructure-Conditioned Surrogate Models for Graded Multiscale Optimization of Mycelium Composites".

Jane: Here's the gist of the paper. The gist The conditioned surrogate model enables accurate predictions of multiscale mechanical behavior for a mycelium-woodchip composite material, even when trained on small datasets, making multiscale simulations tractable and allowing for optimization of functionally graded structures <ref:2607.13688#pg6>.

Tom: How it works The core contribution is the conditioning of a hybrid physics-data surrogate on microstructural variables using a hypernetwork to enable accurate predictions for functionally graded structures.

Jane: This approach is applied to predict multiscale mechanical behavior for a mycelium-woodchip composite material <ref:2607.13688#pg6>.

Tom: The model is then used to optimize a graded multiscale disk, which resulted in reducing the peak stress by 42% compared to one with a random microstructure.

Paper summary: Tom: So this paper is about how to take these complex sustainable materials and actually design them better using simulation. They introduce a way to make data-driven surrogate models work even when you’re trying to optimize something that has many different microstructures, which is what happens in graded materials.

Jane: It sounds like the main problem they're tackling is that the standard data-driven surrogates only work for one fixed microstructure, but when you want to optimize a functionally graded structure, where the microstructure changes all over, you need much more data than just fixing one thing.

Lu: Exactly. They point out that using a surrogate trained on a range of microstructures requires an even bigger dataset than training on just one specific type of material because you have to cover all those variations for optimization.

Meng: So what's their main idea then? What's the core contribution they are making with this work, "Microstructure-Conditioned Surrogate Models for Graded Multiscale Optimization of Mycelium Composites"?

Tom: Well, they solve that by conditioning a hybrid physics-data surrogate directly on the microstructural variables using a hypernetwork. This lets them make accurate predictions of multiscale mechanical behavior even when they’re only trained on small datasets.

Jane: That sounds like it bypasses that massive data requirement problem, which is huge for materials science. They use this conditioned model to make multiscale simulations of functionally graded structures tractable, and they validate it against a full finite element two-dimensional simulation.

Lu: And they show the impact of this. They optimize a graded multiscale disk and managed to reduce the peak stress by forty-three percent compared to one with a random microstructure. That’s a big number when you’re talking about material design for something like mycelium-woodchip composites.

Meng: Wait, so they are not just doing theory here; they are showing that this method is practical for engineering goals. What's the next step they took to make it even more useful?

Tom: They went further than just conditioning on the microstructural variables themselves. They conditioned the network directly on manufacturing variables that can have a complex influence on how that microstructure ends up forming.

Jane: So, if you’re designing something in a factory, you can use those manufacturing inputs to predict the final mechanical performance before you even build it fully? That makes sense for practical application.

Lu: It turns the problem from just figuring out how a material behaves into an optimization loop where you can control the input that creates the microstructure itself. The paper shows this approach is a practical route to engineer the microscale for desired macroscale behavior, and they demonstrate it using mycelium-woodchip composites as their example.

Meng: From an engineering deployment standpoint, conditioning on manufacturing variables is much more realistic than just guessing what the microstructure is going to be in a simulation. What does that look like in practice?

Tom: It means you’re not just optimizing the material properties; you’re optimizing the process parameters—like how woodchips are deposited or how they are oriented—to get the right mechanical result. That’s where the real engineering value is showing up.

Jane: So, to wrap up this segment, it sounds like this paper moves beyond just making a better simulation tool and shows a path for engineers to control the final product's performance by looking at how they make it. This sets up the next part about what these results actually mean for material design in general.

Lu: Right. It moves the focus from passive modeling to active, controllable design through AI-powered surrogates, and that’s a big shift in how we think about complex systems.

Meng: I wonder if this level of control is something that can scale up easily when you move from a small test sample to a full production run.

Tom: We'll see how well the conditioning on manufacturing variables holds up under those real-world constraints in the next part.

Conclusion: Tom: So, looking at this whole paper, "Microstructure-Conditioned Surrogate Models for Graded Multiscale Optimization of Mycelium Composites," it seems like the main message is that data-driven surrogates can be made much more powerful for complex materials if you condition them on the structure itself or on the process inputs.

Jane: I think that’s right. The paper tackles a real hurdle in simulating functionally graded composites where the internal structure is constantly changing, and they show this conditioned approach makes those simulations work even with small datasets.

Lu: It highlights how crucial it is to have microstructure-aware data-driven surrogates for multiscale simulations, because without that conditioning, you're stuck predicting behavior for just one fixed material configuration.

Meng: For someone who just cares about shipping a product reliably, this means we can potentially use AI to guide the manufacturing process itself toward a better mechanical outcome, rather than just testing materials after they’re made.

Tom: It demonstrates the potential that precise control of microstructural variables can bring to sustainable material development and structural design. The reduction in peak stress by forty-three percent is a concrete result showing the method's effectiveness.

Jane: In simple terms, this work shows how AI can help us engineer the tiny details of a material—the microstructure—in a way that directly improves its big-picture mechanical performance.

Lu: It’s about moving toward systems where you aren't just testing materials; you are using models that allow you to actively design the material structure based on what you need.

Meng: I think the future work they imply is scaling this up to more complex, real-world manufacturing processes where those manufacturing variables are even messier than what they simulated.

Tom: Yeah, and Lalam has said that the conditioned surrogate model enables graded multiscale simulations, which is a key capability here. It shows that this architecture can handle the complexity of varying microstructures effectively.

Jane: So we’re looking at a future where AI isn't just predicting outcomes based on existing data, but actively conditioning those predictions on the very structure being designed in real-time or during the optimization process.

Lu: It suggests that the next generation of material design won't be purely empirical; it will be driven by these types of physics-data surrogate models that are aware of both the material properties and how they were made.

Meng: That sounds like a very powerful tool for reducing the trial and error cycle in developing new, complex composites.

Tom: It’s about using AI to make materials smarter from the microscale up, which is where the real innovation in sustainable engineering is heading.

J. Storma, I. B. C. M. Rochaa, S. Schyckb, K. Masaniab, F. P., van der Meera

Delft University of Technology

cs.LG, cond-mat.mtrl-sci, cs.NA, math.NA, physics.comp-ph

Submitted: 2026-07-15

Updated: 2026-10-18

Code: https://github.com/SLIMM-Lab/hyprnn

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 78/100

The gist: The gist The conditioned surrogate model enables accurate predictions of multiscale mechanical behavior for a mycelium-woodchip composite material, even when trained on small datasets, making

Key concepts

Conditioned Surrogate Model: A machine learning model that is specifically tailored or 'conditioned' based on certain input data. In this work, the model is conditioned on microstructural variables (like material properties) or manufacturing variables (like deposition settings). This conditioning allows the surrogate to make highly accurate predictions for complex, functionally graded materials where standard models might fail.
Hypernetwork: A type of neural network used here to condition the main physics-based surrogate model. The hypernetwork acts as a translator, taking microstructural variables or manufacturing inputs as input and generating specific parameters that guide the main prediction network. This allows the system to adapt its behavior based on how the material is structured or how it was made.
Functionally Graded Structures: Materials where properties change gradually across their volume rather than being uniform throughout. The study focused on creating a graded multiscale disk, meaning the mechanical properties transition smoothly from one end to the other, which is achieved by controlling the microstructure along that gradient. This structure was optimized to improve performance.
Multiscale Simulation: A computational approach that models material behavior across different length or time scales simultaneously. The research uses this technique to link microscopic details (like individual fiber arrangement) with macroscopic behavior (like overall stress in a disk), enabling the optimization of the structure from the microscale up to the macroscale.

Terminology

Surrogate Model — 3× in this paper · explained in 3 episodes
Surrogate Models — 3× in this paper · explained in 3 episodes
Hypernetwork — 1× in this paper · explained in 4 episodes

Summary

The gist The conditioned surrogate model enables accurate predictions of multiscale mechanical behavior for a mycelium-woodchip composite material, even when trained on small datasets, making multiscale simulations tractable and allowing for optimization of functionally graded structures <ref:2607.13688#pg6>.

How it works

The core contribution is the conditioning of a hybrid physics-data surrogate on microstructural variables using a hypernetwork to enable accurate predictions for functionally graded structures. This approach is applied to predict multiscale mechanical behavior for a mycelium-woodchip composite material <ref:2607.13688#pg6>. The model is then used to optimize a graded multiscale disk, which resulted in reducing the peak stress by 42% compared to one with a random microstructure.

The HyPRNN architecture is designed to condition the Physics-based Recurrent Neural Network (PRNN) on microstructural variables using a hypernetwork H. The encoder learns to compute microscopic strain quantities from the macroscopic strain input, and these are passed through fictitious material points employing physics-based microscopic material models to produce microscopic stresses. The decoder then combines these microscopic stresses into a macroscopic stress.

The paper introduces two types of encoders for the finite strain PRNN to capture geometric nonlinearity. The linear encoder uses a weight matrix WEm learned for each fictitious material point to compute the microscopic strain Eˆωm = Eomega WEm. This requires satisfying two conditions: first, in the undeformed state, all microscopic strains must vanish (Fomega = I → Eˆωm = 0), and second, to compute the response of the fictitious material points using a neo-Hookean model, Cˆωm must be positive definite. The linear encoder enforces this by scaling WEm when its eigenvalues exceed a limit of 1 to guarantee det(Cˆωm) > 0 for any Fomega.

The nonlinear encoder is designed to satisfy the same two conditions by allowing arbitrary nonlinear operations on the inputs and then constraining the intermediate state. It uses a neural network NNE that takes Eomega as input and outputs 3M variables, which are then mapped to Cˆωm through a Cholesky-style parametrization using a shifted softplus function.

Inspiration and Material Modeling

The work is inspired by applications such as functionally graded bio-based composites, specifically mycelium-woodchip composites. Mycelium is considered a vegetative root-like structure of fungi composed of hyphae with a diameter of about 1 µm. Mechanical tests revealed that its Young’s modulus depends on density, giving an average of E = 1.3 [MPa] for a density of 34 [kg/m3], and Poisson’s ratio ν = 0.275. Woodchips are assumed to have isotropy and standard beech properties with E = 13000 [MPa] and ν = 0.375 [-].

The constitutive behavior of mycelium is commonly modeled using a hyperelastic material model. The energy in 3D for this compressible neo-Hookean formulation is defined as W(F) = µ2(I1 − 3) − µ ln J + λ2(ln J)2. The second Piola-Kirchhoff stress then follows as S = µ (I − C−1) + λ ln J C−1.

Surrogate Training and Validation

The dataset for training the surrogate models is generated by simulating RVEs spanning a range of microstructural parameters. The four parameters considered are the ellipse aspect ratio r, the woodchip volume fraction Vf, the mycelium shear modulus µ, and the ellipse orientation ϕ. The material variable µ is included in the dataset but is not necessary for random ellipse packing of the RVE.

The HyPRNN is implemented in JAX and trained using an L2 loss minimized with the Adam optimizer. The training is done in E-S space because their symmetry allows for reducing the input and output dimensions of the surrogates.

Results and Optimization

The comparison between models on different datasets shows that the linear PRNN performs well in the low-data regime, while the nonlinear PRNN starts from a higher loss but does not suffer the same plateau. The linear HyPRNN with 512 samples showed a near-perfect match in FE2 validation for a graded multiscale beam.

In the graded multiscale optimization of a disk loaded with internal pressure, an efficient uniform parametrization reached a low peak stress of 2.73 [MPa] after 240 simulations. The graded structure further decreased this peak stress to 2.59 [MPa] after 1006 simulations.

Manufacturing Variable Conditioning

The paper demonstrates conditioning the PRNN directly on manufacturing variables that can have a complex influence on the microstructure. This is achieved by conditioning on the inputs of a discrete-element method simulation that creates the microscopic geometry.

The dataset for manufacturing variables includes simulating woodchip deposition using Yade, where pellet fraction and initial orientation are controlled variables. The resulting model was used in an optimization loop to substantially alter the deformation pattern of a sample under compression. The optimized result showed a bulge of 0.00001 compared to a baseline bulge of 1.48251.

Conclusion

The conditioned surrogate model enabled graded multiscale simulations. This work highlights the necessity of microstructure-aware data-driven surrogates for multiscale simulations. Furthermore, it demonstrates the potential that precise control of microstructural variables can bring.

Improvements for AI systems

Conditioning surrogate models on manufacturing variables enables engineering microscale behavior for complex geometries that cannot be parametrized explicitly, which is a practical route to engineer the microscale for desired macroscale behavior. This allows AI systems to design materials where the microstructure is controlled by process inputs rather than relying solely on pre-defined geometric parameters.
Implementing a hybrid physics data surrogate called HyPRNN allows accurate predictions of multiscale mechanical behavior even when trained on small datasets, making multiscale simulations of functionally graded structures tractable. This capability accelerates the development and design of future sustainable materials and structures by enabling optimization with limited simulation data.
The use of a hypernetwork to learn PRNN weights based on microstructural variables allows material parameters to be modified directly in the fictitious material points without requiring retraining or additional data collection. This means AI systems can adapt constitutive models instantly when the underlying microstructure changes, overcoming the limitation that existing surrogates are typically trained for a single, fixed microstructure.
Introducing a nonlinear encoder variant allows capturing geometric nonlinearity in finite strains while satisfying conditions that ensure all microscopic strains to vanish in the undeformed state and that the resulting deformation tensors are valid for a neo-Hookean model. This enhances the accuracy of surrogate models when simulating large deformations, which is crucial for complex material behaviors.
The ability to condition on manufacturing variables such as pellet fraction and woodchip orientation allows AI systems to find manufacturing parameters that lead to desired mechanical behavior, such as minimizing peak stresses in a graded disk simulation where the optimized pattern shows an X-like structure that forms bands from the corners of the sample. This provides a computational proof-of-concept for designing materials based on process control.

Abstract

Emerging sustainable materials increasingly rely on engineered hierarchy and microstructure to achieve control of their properties and mechanical behavior. Optimizing these materials with controllable microstructures requires efficient multiscale simulations. Data-driven surrogate models for the microscale can accelerate multiscale simulations, but require large amounts of data even for a fixed microstructure. When a range of microstructures is considered, as is the case in multiscale optimization, even more data is needed to train a surrogate. To overcome this challenge, we condition a hybrid physics-data surrogate on microstructural variables using a hypernetwork. This approach enables accurate predictions of multiscale mechanical behavior for a mycelium-woodchip composite material, even when trained on small datasets. The conditioned surrogate makes multiscale simulations of functionally graded structures tractable, and we validate it against a full FE squared simulation. We optimize a graded multiscale disk, and reduce the peak stress by 43% compared to one with a random microstructure. Then, we go one step further, conditioning the network directly on manufacturing variables that can have a complex influence on the microstructure. This is a practical route to engineer the microscale for desired macroscale behavior. This contribution highlights the benefits of microarchitectured structures and demonstrates how conditioned surrogate models enable their multiscale optimization, which will accelerate the development and design of future sustainable materials and structures.