PA-SciML: Auditing Scientific Machine Learning for Physics

Scientific machine learning has a trust problem: a neural surrogate can fit training data beautifully and still violate the physics it's supposed to describe. A new workflow called Physics-Audited Agentic SciML (PA-SciML) tackles this by making physics compliance a pass/fail requirement, not an afterthought. The idea is simple to state and surprisingly rare in practice: before any model gets picked, its outputs are checked against explicit, machine-checkable physics requirements.

What "Physics-Audited" Actually Means

Most explanations of verification in scientific machine learning stop at "check the error." PA-SciML does something more specific. The workflow fixes a scoring evaluator before the search begins, and from that derives reviewable, machine-checkable physics requirements. Each trained candidate model is then checked on its actual outputs for things like boundary conditions, superposition, stiffness scaling, and causality — not just whether its predictions land close to the data.

The workflow also adds advisory numerical probes before training and deliberately tests one modeling change at a time, so every score gain can be traced back to an isolated, recorded edit. That's an audit trail, not just a leaderboard.

Where the Baseline Fails: Causality

The clearest evidence comes from two sets of computational solid mechanics examples. In static elasticity runs, both the PA-SciML-selected surrogate and an error-only baseline pass common linear-elastic checks — but the selected surrogate achieves lower validation error. So even where the baseline survives, physics auditing doesn't cost you accuracy; here it came with better error too.

The transient elastodynamics runs are where the distinction really matters. There, the error-only baseline fails a stricter causality check by responding to future parts of the loading history — meaning the model was effectively peeking ahead in time to produce its answers. The PA-SciML-selected surrogate passes the stated checks. An error-only evaluation would never have caught that failure on its own; low error and violated causality can coexist perfectly comfortably.

Why Auditing Before Search Changes the Game

Here's what I think most coverage of agentic scientific ML glosses over: an agent that searches over models is only as trustworthy as its selection criterion. If that criterion is validation error alone, the agent will happily select a physically nonsensical model that happens to fit well — and in transient problems, one that violates causality while doing it. PA-SciML's real contribution isn't a new model architecture; it's fixing the evaluator first and making every requirement reviewable before training starts.

It's easy to conflate this with PINNs (physics-informed neural networks), where physics is baked into the loss during training. That's a different mechanism — PA-SciML audits outputs after training against explicit requirements derived up front, which means failures are visible as failures rather than smoothed into gradients.

What this actually points to is a shift in how we should evaluate agentic workflows in science generally: not by whether the agent produces impressive numbers, but by whether its acceptance criteria are written down early enough that humans can review them — and strict enough that they catch things like temporal peeking that raw error scores structurally cannot see.