Open problems

Every design problem we take on asks the same four questions.

Metamaterials answer all four in one line of work. A procedural language describes the geometry. Fifty hand-written programs grow into a database of 150,000 through sampling, mutation, and hybridization, which is how thin data becomes enough. A model then writes a program from a plain-language specification of the properties you want, and the program is simulated to check whether it delivered them. What gets printed and pulled on the bench decides whether the simulator was telling the truth.

The domains change. Metamaterials, molecules, robots, drones, printers. The questions do not. That is the point of working across unrelated fields: a representation or a solver that holds up in only one domain has probably fit that domain's quirks rather than found something general. Each new field is a test of whether the method is real, and it sets who does well here: people who would rather learn a new field than reuse a familiar one.

Three questions drive the group today. Each one is open, funded, and taking new students.

01

Domain-specific languages for design

Design languages that capture the world, and AI that designs within those languages

Programs, not pixels. We build design languages that a machine can write and a solver can check, so that a generated artifact is correct by construction rather than plausible by appearance.

What you would work onSolver-aided languages for LLM-driven CAD, procedural graph representations, and program synthesis for materials. Suits people who care about both program semantics and the geometry that comes out the other end.

MetaGen: A DSL, Database, and Benchmark for VLM-Assisted Metamaterial Generation 2025preprint Procedural Metamaterials: A Unified Procedural Graph for Metamaterial Design 2023 A Solver-Aided Hierarchical Language for LLM-Driven CAD Design 2025 VLMaterial: Procedural Material Generation with Large Vision-Language Models 2025

02

Neural physics surrogates

From a design to its performance, and back again

Learned simulators that preserve physical structure and can be checked against a classical solver. The aim is models that replace or accelerate those solvers without discarding the constraints and invariants that make them trustworthy.

What you would work onModular neural simulators, differentiable physics, and scalable contact. Expect numerical methods alongside deep learning, not one instead of the other.

GeoPT: Scaling Physics Simulation via Lifted Geometric Pre-Training 2026preprint Neural Modular Physics for Elastic Simulation 2025preprint M-ABD: Scalable, Efficient, and Robust Multi-Affine-Body Dynamics 2026

03

AI for scientific discovery

Find the limits of design, then break them

Closing the loop from hypothesis to experiment. Discovery systems that propose candidates, run them on real instruments, and learn from what actually came back.

What you would work onAutonomous experimentation for materials, molecules, proteins, and the instruments themselves. Suits people who want a result they can hold, and who are willing to wait on an instrument to produce it.

Computational discovery of extremal microstructure families 2018 Computational discovery of microstructured composites with optimal stiffness-toughness trade-offs 2024 Accelerated discovery of 3D printing materials using data-driven multiobjective optimization 2021

Part of the archive the next systems stand on: measured reflectance, neural holography, mechanical characters, a printed hand.

The near-term version is a design language and a copilot for each domain we work in: a small, readable language that describes the domain in its own vocabulary, a model that writes programs in that language from a plain-language brief, and a compiler and solver that check the result before anything is built. The output is a program rather than an answer, which means it can be read, tested, versioned, and rejected.

The harder problem is designing beyond data. AI trained on what worked learns the patterns of what worked: it copies, refines, and optimizes, which is useful right up until the answer lies outside the pattern. And the rules that constrain a design hardest are the ones nobody wrote down, the assumptions baked in deep enough to pass for truth. We are building systems that treat those assumptions as the rules of a game rather than as facts, and that can work out which ones are worth breaking. In our own soft-robot benchmark, an evolved design jumped higher than anything the group had built by hand, in a shape nobody would have drawn. That problem is open, and it is the one we would most like to solve. Success would be a partner rather than a brilliant apprentice: a system that does not only answer the question it was handed but asks whether the frame around it is right, and that can tell which of our assumptions are load-bearing and which are only habits. The measure is whether that produces the kind of shift climate change, pandemics, and scarcity actually demand, rather than a faster version of what we already know how to build.

The three open problems above rest on long-running work in computer graphics, computational design and fabrication, computer vision, and robotics. Each strand below opens the papers behind it. The measurements behind the reflectance work are public as the MERL BRDF database.