Stop Optimizing RMSE Alone: How to Evaluate Scientific AI Systems for Real Decision Value

Perspective: I am bullish on ML for science, but skeptical of benchmark-driven claims that ignore physical validity and downstream decision impact. In scientific workflows, a model is useful only if it is fast enough, calibrated enough, and trustworthy enough for the actual decision being made.

A recurring failure mode in scientific ML is simple: teams report a single error metric (often RMSE), celebrate a gain, and then discover the model is unreliable in exactly the edge regimes that matter for experiments or operations.

If your model helps choose experiments, tune process conditions, or de-risk expensive simulations, your evaluation protocol has to go beyond average prediction error.

The core mistake: treating scientific modeling like generic leaderboard ML

For many scientific tasks, objective quality is multidimensional:

1. Numerical accuracy (e.g., MAE/RMSE),
2. Physical consistency (constraints/invariants),
3. Uncertainty quality (calibration/coverage),
4. Decision utility (does it improve what humans do next?),
5. Runtime/cost (can it be used in real loops?).

A model can score well on (1) and still fail badly on (2)-(5).

A practical 5-layer evaluation stack

Layer 1 — Accuracy by regime, not just global average

Always stratify by meaningful regimes:

• interpolation vs extrapolation,
• low-noise vs high-noise conditions,
• nominal vs rare/extreme boundary conditions.

Report percentiles, not only means. A low mean error can hide catastrophic tails.

Layer 2 — Physics and constraint compliance

Track explicit violation rates:

• conservation laws,
• boundary condition adherence,
• monotonicity/symmetry constraints where applicable.

If violation rates are non-trivial, you need either constrained decoding, physics-informed regularization, or fallback to trusted solvers.

Layer 3 — Uncertainty calibration (not just point predictions)

In scientific decision-making, uncertainty is not decoration; it controls risk.

Evaluate:

• reliability diagrams,
• expected calibration error (ECE),
• conformal coverage under distribution shift,
• sharpness vs coverage trade-off.

A model with calibrated uncertainty can be safely integrated with abstention/fallback policies.

Layer 4 — Counterfactual decision utility

This is the layer teams skip most often.

Ask: Would this model have changed decisions in a beneficial way on historical cases?

Examples:

• fewer failed experiments for same budget,
• faster convergence to high-performing process parameters,
• lower false confidence in risky operating zones.

Even a slightly less accurate model can be preferable if it yields better action quality under constraints.

Layer 5 — Operational robustness and economics

Measure production reality:

• p50/p95 latency,
• throughput under burst traffic,
• fallback rate to full simulation,
• cost per accepted decision (not just cost per inference).

In many organizations, this layer determines whether the model survives beyond a pilot.

Suggested scorecard template

Treat this as a deployment gate, not a documentation artifact.

Implementation pattern that works in practice

A reliable pattern is a hybrid control policy:

1. Use surrogate model for fast candidate screening.
2. Require confidence + constraint checks.
3. Escalate uncertain or high-impact cases to full simulator.
4. Log failures and active-learning candidates.

Pseudo-policy:

python
def decide(x):
    y_hat, u = surrogate.predict_with_uncertainty(x)
    if violates_constraints(y_hat):
        return full_solver(x), "fallback:constraint"
    if u > uncertainty_threshold:
        return full_solver(x), "fallback:uncertainty"
    return y_hat, "surrogate"

This architecture usually outperforms "surrogate-only" systems in real scientific workflows.

Common anti-patterns

• Single split validation on temporally correlated data.
• No stress tests on out-of-regime conditions.
• No lineage tracking linking model version to data and preprocessing version.
• No decision-level KPI, only model-level metrics.

If these are missing, the reported performance is likely optimistic.

What to do in the next 30 days

1. Add regime-stratified evaluation and tail metrics.
2. Define at least one explicit physics-violation KPI.
3. Add calibration diagnostics and an abstention threshold.
4. Run backtests on historical decisions, not just prediction labels.
5. Publish a one-page deployment gate with metric thresholds.

Bottom line

For scientific AI systems, the right question is not "Is this model more accurate?" It is "Does this system improve scientific decisions while respecting physics, uncertainty, and operational constraints?" Teams that evaluate at the system level — not just the model level — are the ones that ship reliably.

References

1. M. Raissi, P. Perdikaris, G. Karniadakis, Physics-informed neural networks, Journal of Computational Physics (2019). https://www.sciencedirect.com/science/article/pii/S0021999118307125
2. Z. Li et al., Fourier Neural Operator for Parametric PDEs, ICLR (2021). https://arxiv.org/abs/2010.08895
3. L. Lu et al., Learning nonlinear operators via DeepONet, Nature Machine Intelligence (2021). https://www.nature.com/articles/s42256-021-00302-5
4. A. N. Angelopoulos, S. Bates, A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification (2021). https://arxiv.org/abs/2107.07511
5. C. Guo et al., On Calibration of Modern Neural Networks, ICML (2017). https://arxiv.org/abs/1706.04599
6. JAX project documentation. https://github.com/jax-ml/jax
7. NVIDIA PhysicsNeMo documentation. https://docs.nvidia.com/physicsnemo/