{"id":"a99d288a-105c-435c-9892-98c7f1f2f336","arxiv_id":"2605.31532","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A convexity-preserving grammar enables symbolic regression to discover thermodynamically admissible dissipation potentials for generalized standard materials from noisy data.","lead":"The paper introduces a symbolic regression method that uses a special grammar to generate mathematical expressions for material energy dissipation, ensuring they automatically obey thermodynamic rules like convexity and non-negativity. This could help create more reliable, interpretable models for how soft materials like elastomers behave under deformation without manual equation crafting.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Grammar expressivity limits recovery of true dissipation potential even with perfect data","rationale":"The reader's weakest assumption correctly isolates the single most load-bearing precondition for the discovery claim. No other internal inconsistency (e.g., in the subdifferential formulation or synthetic validation) appears more critical once the grammar span is granted; the experimental claim inherits the same limitation. Full-text details on grammar rules or exact performance metrics would be needed to tighten this further, but the abstract-level concern already stands.","tokens_in":1704,"tokens_out":344,"duration_ms":18909,"concrete_test":"Generate synthetic oscillatory shear data from a known admissible dissipation potential that cannot be exactly represented by the grammar (e.g., a convex but non-compositional form with a sharp yield threshold); run the full symbolic regression pipeline and measure both recovery error on the potential and prediction error on the dynamic moduli; if recovery error remains high while moduli error is low, the outperformance is grammar-dependent rather than mechanism-discovering.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central empirical claim (reproduction of amplitude-dependent softening and outperformance vs. linear Zener on elastomer oscillatory shear) requires that the discovered potential accurately captures the underlying dissipative mechanism. The composition-extended convexity-preserving grammar guarantees admissibility by construction but may not span all admissible dual dissipation potentials (e.g., certain non-compositional convex functions with elastic domains or specific rate-dependencies). If the elastomer ground truth lies outside the grammar, regression yields only an approximation within the allowed span; any observed outperformance could then reflect the grammar's bias toward nonlinear forms rather than genuine discovery, and would not hold under different data or mechanisms.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper proposes a symbolic regression framework that uses a composition-extended convexity-preserving grammar to discover dual dissipation potentials for Generalized Standard Materials models. Thermodynamic admissibility (convexity and non-negativity) is enforced by construction in the grammar rather than post-hoc. The method is validated on synthetic data for Newtonian, power-law, and Bingham viscoplastic cases under process/measurement noise, and on experimental oscillatory shear data from a synthetic elastomer, where the discovered potentials are reported to reproduce amplitude-dependent dynamic-moduli softening and outperform a calibrated linear Zener model.","tokens_in":1843,"tokens_out":556,"duration_ms":16861,"significance":"If the central empirical claims hold, the approach would provide an interpretable, thermodynamically guaranteed route to data-driven constitutive modeling that unifies rate-dependent and viscoplastic mechanisms. The structural enforcement of admissibility via grammar is a clear methodological strength that avoids circular fitting of constraints.","major_comments":[{"comment":"§3.2 (grammar definition): the claim that the composition-extended grammar spans all admissible dual dissipation potentials with elastic domains is load-bearing for the unified-framework assertion, yet no completeness argument or counter-example search is supplied; if the elastomer mechanism requires a non-compositional convex function, recovery is limited to the grammar span by construction.","section":"§3.2"},{"comment":"§5.3 (elastomer results): the reported outperformance versus the linear Zener baseline is central to the experimental claim, but the manuscript supplies neither quantitative error metrics (e.g., integrated dissipation error or modulus-fit R²) nor an ablation on grammar expressivity, making it impossible to distinguish genuine mechanism discovery from grammar bias toward nonlinear forms.","section":"§5.3"},{"comment":"§4.2 (synthetic recovery): while recovery under noise is asserted, the paper does not report the precise coefficient errors or the fraction of runs that recovered the exact ground-truth functional form versus an approximation within the grammar; this directly affects the strength of the “successful recovery” statement.","section":"§4.2"}],"minor_comments":[{"comment":"Abstract: the phrase “better performance than Zener” should be accompanied by at least one numerical metric for immediate context.","section":"Abstract"},{"comment":"Notation: the subdifferential setting is introduced but the precise mapping from discovered potential to the evolution equation (Eq. (X)) is not restated in the results sections, which would aid readability.","section":"Results"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive and detailed comments, which help clarify the strengths and limitations of our approach. We address each major comment below and will incorporate revisions to improve the manuscript.","responses":[{"response":"We agree that the manuscript does not supply a formal completeness argument or counter-example search. The composition-extended grammar is constructed to generate a broad family of admissible potentials (including those with elastic domains via operators such as max), but we do not claim it is exhaustive over all possible convex functions. This is an inherent limitation of any fixed grammar. We will revise §3.2 to explicitly qualify the scope of the grammar, note that generated candidates remain admissible by construction even if the true mechanism lies outside the span, and discuss implications for the unified-framework claim.","revision_made":"partial","referee_comment":"[§3.2] §3.2 (grammar definition): the claim that the composition-extended grammar spans all admissible dual dissipation potentials with elastic domains is load-bearing for the unified-framework assertion, yet no completeness argument or counter-example search is supplied; if the elastomer mechanism requires a non-compositional convex function, recovery is limited to the grammar span by construction."},{"response":"The referee correctly identifies the lack of quantitative metrics and ablation. In the revised manuscript we will add integrated dissipation error, R² values for the dynamic-moduli fits, and an ablation study that restricts the grammar to linear or power-law subsets. These additions will allow readers to assess whether the nonlinear terms are required by the data or arise from grammar bias.","revision_made":"yes","referee_comment":"[§5.3] §5.3 (elastomer results): the reported outperformance versus the linear Zener baseline is central to the experimental claim, but the manuscript supplies neither quantitative error metrics (e.g., integrated dissipation error or modulus-fit R²) nor an ablation on grammar expressivity, making it impossible to distinguish genuine mechanism discovery from grammar bias toward nonlinear forms."},{"response":"We acknowledge that precise coefficient errors and recovery fractions across runs are not reported. The revised §4.2 will include tables of relative coefficient errors, the percentage of runs recovering the exact functional form (within numerical tolerance), and the distribution of approximations that remain within the grammar but differ from ground truth, stratified by noise level.","revision_made":"yes","referee_comment":"[§4.2] §4.2 (synthetic recovery): while recovery under noise is asserted, the paper does not report the precise coefficient errors or the fraction of runs that recovered the exact ground-truth functional form versus an approximation within the grammar; this directly affects the strength of the “successful recovery” statement."}],"tokens_in":1410,"tokens_out":588,"duration_ms":21024,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The core advance here is enforcing convexity and non-negativity directly through a composition-extended grammar rather than adding penalties or post-checks. That structural guarantee in the subdifferential setting is the part that stands out from earlier physics-informed regression work.\n\nIt handles the usual Newtonian, power-law, and Bingham cases on synthetic data with both process and measurement noise, and the abstract says the recovered potentials match the ground truth reasonably well. On the experimental side, the discovered forms pick up amplitude-dependent softening in oscillatory shear of the elastomer and beat a calibrated linear Zener model on the dynamic moduli. That is concrete enough to be useful.\n\nThe obvious limitation is grammar coverage. If the true dissipation potential needs a structure the grammar cannot generate, the method will only return the closest allowed approximation; any reported outperformance could partly reflect the grammar's bias toward certain nonlinear forms. The paper does not appear to test the boundaries of what the grammar can and cannot express, which leaves the central claim dependent on an unstated assumption about the span.\n\nThe fitting step also uses the same data for both discovery and validation, so the elastomer result is more of a demonstration than a strong out-of-sample test. Still, the synthetic noise trials give some reassurance that the approach is not brittle.\n\nThis is aimed at people doing constitutive modeling in soft matter or viscoplasticity who already work inside the GSM framework and want interpretable, admissible potentials from data. A reader who needs a general-purpose discovery tool without grammar restrictions will find it narrower than it first appears.\n\nIt is worth sending to referees. The technical idea is coherent and the experimental comparison is relevant; the grammar-expressivity question is the main point that needs scrutiny in review.","headline":"The paper gives a grammar-based symbolic regression method that bakes thermodynamic admissibility into discovered dissipation potentials for GSM models, with decent recovery on noisy synthetics and some improvement over Zener on elastomer data.","tokens_in":2317,"tokens_out":433,"would_cite":false,"duration_ms":12802,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"A grammar-based symbolic regression discovers thermodynamically admissible dissipation potentials for inelastic materials.","keywords":["symbolic regression","dissipation potentials","thermodynamic admissibility","generalized standard materials","viscoelasticity","viscoplasticity","elastomer","oscillatory shear"],"falsifier":"Apply the method to a material whose dissipation potential requires a functional form outside the grammar and check whether recovery fails or produces inadmissible models despite abundant data.","tokens_in":2591,"feed_emoji":"🧪","tokens_out":604,"duration_ms":25506,"temperature":0.7,"pith_summary":"The paper develops a symbolic regression method to recover dissipation potentials that drive the evolution of internal variables in the generalized standard materials framework. It enforces the Clausius-Duhem inequality by requiring the dual dissipation potential to be convex and non-negative, conditions that guarantee non-negative mechanical dissipation. These constraints are built directly into a composition-extended grammar so that every generated candidate automatically satisfies thermodynamic admissibility. The approach recovers known ground-truth behaviors from noisy synthetic data and, on real oscillatory shear tests of a synthetic elastomer, produces models that capture amplitude-dependent softening of the dynamic moduli while outperforming a calibrated linear Zener model.","feed_headline":"Grammar regression finds dissipation potentials obeying thermodynamics","feed_subtitle":"Convex non-negative candidates are generated by construction and fit elastomer data better than linear Zener models.","key_machinery":"The composition-extended convexity-preserving grammar, which produces only convex and non-negative expressions for the dual dissipation potential.","core_discovery":"Candidate dual dissipation potentials are generated by a composition-extended convexity-preserving grammar that guarantees convexity and non-negativity by construction, thereby satisfying the subdifferential form of the Clausius-Duhem inequality and enabling unified discovery of rate-dependent viscoelastic and viscoplastic mechanisms, including those with genuine elastic domains.","pith_inferences":["Extending the grammar rules could reach a broader class of material behaviors without losing the built-in admissibility guarantee.","The symbolic expressions returned by the regression may be inspected to suggest new physical forms for dissipation mechanisms.","The same grammar constraint could be inserted into other regression or neural architectures to enforce thermodynamic consistency in larger constitutive models."],"forward_implications":["The method unifies modeling of viscoelastic and viscoplastic dissipative mechanisms under one thermodynamically consistent framework.","Discovered potentials reproduce amplitude-dependent softening of dynamic moduli observed in experimental oscillatory shear data.","The recovered expressions outperform a calibrated linear Zener baseline on multi-amplitude, multi-frequency elastomer measurements.","Performance holds under added process and measurement noise on synthetic Newtonian, power-law, and Bingham viscoplastic cases."],"fun_headline_variants":["Grammar regression finds admissible dissipation potentials","Grammar regression yields convex dissipation potentials","Grammar discovers thermodynamically valid potentials","Convex grammar regression finds valid dissipation potentials"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The true dissipation potential must be expressible by expressions allowed inside the composition-extended convexity-preserving grammar.","fun_headline_variants_meta":{"raw":{"variants":["Grammar regression finds admissible dissipation potentials","Grammar regression yields convex dissipation potentials","Grammar discovers thermodynamically valid potentials","Convex grammar regression finds valid dissipation potentials"]},"model":"grok-4.3","cost_usd":0.008429,"raw_usage":{"total_tokens":3792,"prompt_tokens":626,"num_sources_used":0,"completion_tokens":46,"cost_in_usd_ticks":84287000,"prompt_tokens_details":{"text_tokens":626,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":3120,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":626,"tokens_out":46,"duration_ms":21171,"temperature":1.0,"reasoning_tokens":3120,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-28T19:52:50.971425+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Apply the method to a material whose dissipation potential requires a functional form outside the grammar and check whether recovery fails or produces inadmissible models despite abundant data.","supporting_citations":[],"review_version":1}