Physics-Constrained Learning for Reduced-Order Thermoacoustic Stability Screening: Locating Instability Boundaries from Few Evaluations

High-fidelity prediction of thermoacoustic instability in combustors — for example through reactive Large-Eddy Simulation (LES) — is accurate but expensive: each operating point can cost days to weeks of computation, so mapping a stability boundary across a design space is often prohibitive. This paper presents a physics-constrained learning approach, here designated Constrained-by-Physics Learning (CPL), and demonstrates its use as a cheap, physically consistent pre-screen that locates instability boundaries from very few evaluations. CPL is formulated as a single projection onto the manifold of states admissible under a governing operator, and is shown to have two equivalent faces: a causal (light-cone) mask applied to an attention operator, and a physics-residual penalty added to a fitting objective. Using a reduced-order thermoacoustic model of a generic combustor (a one-dimensional acoustic network closed by a Crocco n–tau flame-transfer function), we show that CPL (i) recovers a quarter-wave acoustic mode from a handful of noisy samples where an unconstrained regression diverges, and (ii) locates the marginal-stability flame gain from four noisy evaluations with an accuracy (1.99 ± 0.12) far exceeding a physics-free cubic fit (2.04 ± 0.58), recovering the same boundary that the full reduced model obtains from a fifteen-point sweep. All models, code and data are generic and fully reproducible; no proprietary geometry or calibration is used. The method is offered as a tool to make expensive high-fidelity campaigns efficient, by identifying in advance which operating points warrant full resolution.