The arXiv preprint Discovering Thermodynamically Admissible Dissipation Potentials via Grammar-Based Symbolic Regression, posted this week, does something quietly important: it teaches a machine to invent material laws — and refuses to let the machine cheat. The authors build a symbolic-regression engine whose grammar is wired so that every candidate formula it can produce is already convex, non-negative, and therefore guaranteed to satisfy the Clausius–Duhem inequality. The discovered laws are not just accurate. They are admissible by construction.

←TODAY: A 2026 arXiv paper validates the framework on Newtonian, power-law, and Bingham viscoplastic synthetic data and on real oscillatory-shear measurements of a synthetic elastomer — the discovered potentials reproduce amplitude-dependent softening and beat a calibrated linear Zener baseline.
→3012: Every load-bearing element on a Zurich-3012 site carries its own discovered constitutive law, written in symbolic form, signed by a physics certificate, and edited by the building itself when material behaviour drifts.
Fulcrum: An interpretable material law is only worth its second-law guarantee. Readability without thermodynamic admissibility is just a confident lie in LaTeX.

The system behind the signal

The Generalized Standard Materials (GSM) formalism is the spine here. It says every dissipative material — viscoelastic damper, fresh-concrete extrusion, lead-rubber bearing, creeping CLT panel — can be described by two scalar potentials, one elastic, one dissipative. The dual dissipation potential the paper hunts governs how internal variables evolve in time. The Clausius–Duhem inequality requires that potential be convex and non-negative on stress space; that is what keeps mechanical dissipation non-negative.

Most data-driven constitutive models — neural ODEs, PINNs of the last six years — bury that requirement inside a loss term, or inside an architecture you cannot read. The grammar in this paper does the opposite. Every production rule preserves convexity. The output is a symbolic expression a structural engineer can read, hand-check, and drop into a finite-element solver the next morning.

Where it lands on your desk

Three concrete places this matters this week. First, mass-timber: CLT creep is notoriously hard to fit across long timescales without overfitting. Second, seismic isolation: lead-rubber bearings and high-damping elastomers show amplitude-dependent softening — the Mullins effect — and your reference Zener model is wrong above ~30 % strain. Third, 3D-printed concrete: Bingham viscoplastic flow drifts with mix design, and your slicer’s deposition rate depends on it. In all three, a discovered law you can read — and that cannot violate thermodynamics — is more useful than a 200 MB neural network you cannot ship to a regulator.

Building-sense: A building running this would feel its own dampers learning. An accelerometer triggers an oscillatory-shear identification overnight; by morning the building’s twin has a new symbolic expression for its bearings’ dual dissipation potential — three terms, readable, signed, and quietly substituted into the next solver step.

Atelier: Drop the framework next to PAZ’s structural-health-monitoring kit. Feed it a year of strain-gauge data from a Zürich footbridge. The artefact you ship to the responsible engineer is one line of LaTeX, not a checkpoint file.

The trade-off is real and the authors do not hide it: grammar-bound search is slower than gradient fitting, and a grammar that excludes whole classes of admissible potentials — non-separable terms, hidden singularities — will silently miss the right answer. The discipline is in choosing the grammar honestly.

For the deeper twin frame, see PAZ’s Digital Twin — En Ingenieria concept panel: a twin earns its keep when it stops being a museum dashboard and starts recommending interventions. A symbolic, thermodynamically-bounded constitutive law is exactly the kind of object a recommending twin can stand on. Contrast this with the Leiden Declaration on AI in mathematics, covered by Ars Technica last week — the worry there is opaque, attribution-stripping AI eroding proof integrity. The arXiv paper is the counter-example: AI doing symbolic work a human can read, audit, and own.

Hack: verify a dissipation potential by hand

This Hack teaches you to check, in five lines, that a dual dissipation potential is thermodynamically admissible — the second-law constraint that makes any discovered material law trustworthy.

import numpy as np
# Bingham viscoplastic dual dissipation potential phi*(sigma)
def phi_dual(sigma, sigma_y=2.0, eta=0.1):
    excess = np.maximum(0.0, np.abs(sigma) - sigma_y)
    return 0.5 * excess**2 / eta
sigma = np.linspace(-5, 5, 1001)
eps_dot = np.sign(sigma) * np.maximum(0.0, np.abs(sigma) - 2.0) / 0.1
print("min mechanical dissipation:", float((sigma * eps_dot).min()))  # >= 0

Read it: yield stress 2.0, viscosity 0.1, strain rate ε̇ emerges by subgradient of the dual potential, and mechanical dissipation σ·ε̇ is non-negative everywhere on the sweep. Swap in your discovered grammar expression and run the same check. If the minimum is negative, the grammar leaked.

This week, pick one inelastic element in your model — a damper, a creep joint, a bearing pad — and draw its real material-law dependency graph. Not the catalogue datasheet: the actual chain of fits, calibrations, and unspoken assumptions that holds its constitutive model in place. The first single point of failure you find is the whole point of the exercise.

Source: arXiv search · Construction as system