Do not judge an AI-generated physics result by how confidently it is written. Verify it by rebuilding the problem, checking the physics, reproducing the computation, quantifying uncertainty, and obtaining independent technical review. If essential inputs, code, assumptions, or tolerances are missing, the scientifically correct label is unverified, not “probably right.”
What “verified” means for an AI physics answer
Verification is a bounded claim: a result is verified only for a stated model, set of inputs, computational method, and tolerance. It does not mean that an answer is universally true or that the language model understands the physics. A derivation can be algebraically flawless while starting from an invalid physical model. A simulation can converge numerically while solving the wrong equations. An experiment can measure a genuine effect while lacking calibration or an uncertainty budget.
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Use four separate questions:
- Is the physical model appropriate? Do the governing equations, assumptions, coordinate system, and boundary conditions describe the regime being studied?
- Is the calculation correct? Are the algebra, numerical implementation, units, signs, and vector operations correct?
- Can another person reproduce it? Are the inputs, code or explicit calculation steps, parameters, intermediate outputs, and software environment available?
- How strong is the evidence? Are uncertainty, sensitivity, independent checks, and outside review sufficient for the conclusion being claimed?
Fluent prose is evidence of neither physical validity nor numerical correctness. Treat the model response as a claim that must be reconstructed.
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Start by preserving the answer exactly as received. Editing a prompt, rounding an input, or regenerating a response can change the result and make later checking impossible.
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Record the response context
- Copy the complete AI output, including equations, code, tables, units, caveats, and any stated confidence.
- Record the tool or model name, version if available, date and time, and the full prompt.
- Save attached files, images, data, system instructions that affect the task, and the requested precision.
- Record settings such as temperature, random seed, sampling controls, tool calls, and whether the answer was regenerated.
- Note every human edit made after generation. Keep the original separate from the edited analysis.
For an AI-assisted analysis, disclose which tool and model version were used, where they were used, and the extent of human oversight. The Centers for Disease Control and Prevention advises authors to document that involvement and, where available, to use tools that embed C2PA metadata as an additional signal of AI-generated content. Metadata supports provenance; it does not validate the physics.
Freeze the numerical inputs
Put all quantities in a machine-readable record before recalculating. Include units, sign conventions, coordinate orientation, reference frames, constants, material properties, initial conditions, and boundary conditions. If a value came from a measurement, retain the raw value and its stated uncertainty rather than only the rounded number shown in the response.
2. Reconstruct the physical problem before checking the answer
Rewrite the task independently of the AI wording. This exposes hidden assumptions and prevents the model’s narrative from becoming your specification.
State the governing law
Identify the equations that actually define the problem: for example, Newton’s laws, Maxwell’s equations, a wave equation, a conservation law, a constitutive relation, or a statistical model. Define every symbol and its units. If the AI jumps directly to a formula, derive or cite the formula’s conditions of validity before using it.
Specify geometry and conventions
Draw the system and state the coordinate axes, origin, positive directions, reference time, and sign convention. Mark forces, fields, fluxes, interfaces, and control surfaces. Many apparently mysterious AI errors are a reversed axis, a missing vector component, or a quantity treated as a scalar when it is directional.
List conditions and approximations
- Initial and boundary conditions.
- Material properties and whether they are constant, isotropic, linear, or temperature-dependent.
- Approximations such as small-angle, incompressible, nonrelativistic, weak-field, steady-state, or point-particle assumptions.
- The domain and regime in which each equation is valid.
- Any neglected interaction, dissipation, coupling, or higher-order term.
Then ask whether the stated data determine a unique solution. An AI may silently invent an initial condition or substitute a typical constant. If the problem is underdetermined, the correct output is a range, a parameterized expression, or a request for missing information—not a precise-looking single number.
3. Run physics checks before arithmetic
Dimensional consistency
Check the dimensions of every additive term and both sides of every equation. A velocity cannot be added to an energy; a force expression must reduce to mass times acceleration; an exponent, logarithm, sine, and cosine must receive a dimensionless argument. Perform the check symbolically before inserting numbers so that a compensating numerical mistake cannot hide a unit error.
Convert units only once, at a documented boundary in the calculation. Track prefixes, squared or cubed units, angular frequency versus ordinary frequency, and degrees versus radians. A result that fails dimensional analysis is wrong regardless of how plausible its decimal representation looks.
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Signs, vectors, and orientations
Verify vector directions with a free-body diagram or component calculation. Check cross-product order, dot-product use, handedness of coordinate systems, and the sign of work, charge, potential, and flux. Re-derive any minus sign that comes from a convention rather than accepting the AI’s explanation.
Conservation laws
Where the model permits it, test conservation of energy, momentum, angular momentum, charge, mass, or probability. Include the exchange with an environment: friction, radiation, external work, heat, or a driven source can make a subsystem’s quantity nonconserved while the larger system remains conserved. A failed conservation check identifies either an omitted interaction, a coding error, or an invalid assumption.
Limiting and special cases
Push the expression toward regimes with known behavior. Set a mass, charge, coupling, or perturbation to zero; take a short-time, long-time, low-speed, large-distance, or weak-field limit; or compare identical bodies where symmetry predicts cancellation. Check continuity at boundaries between approximations. An expression that diverges where the physical model should be regular, changes behavior in the wrong limit, or violates a symmetry needs correction before numerical evaluation.
Order-of-magnitude and scale
Estimate the answer using rounded inputs and powers of ten. Compare it with characteristic scales such as a transit time, thermal energy, wavelength, escape speed, or known material range when those scales are relevant. Order-of-magnitude checking catches misplaced powers, incorrect prefixes, and a formula applied outside its regime without requiring a full reimplementation.
Check assumptions against the regime
A small-velocity approximation cannot be used when the predicted speed is a substantial fraction of the speed of light. A continuum model may fail at microscopic scales, and a linear response may fail near saturation. Let the result test its own assumptions: if a “small” parameter comes out large, rerun the problem with a model valid in that regime or report the limitation.
4. Recalculate independently
Independence matters. Repeating the AI’s exact steps can reproduce its mistake. Choose a method with a different failure mode whenever practical.
Hand algebra or a fresh derivation
Derive the result from the governing equations without looking at the AI’s intermediate steps. Keep symbolic factors until the end, then substitute the frozen inputs. Compare each intermediate quantity, not only the final number. A disagreement localizes the first divergent step.
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Use a computer algebra system or a second human derivation to expand, factor, differentiate, or simplify the expression. Substitute the original equation back into the governing law. Symbolic agreement verifies algebraic equivalence, not the physical assumptions behind the equation.
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Independent numerical implementation
Write a minimal second implementation in a different language, library, or algorithm. For example, compare a closed-form solution with numerical integration, or compare two independently written integrators. Use test cases with known solutions, deliberately extreme values, and a zero-input case. Keep source code, dependency versions, compiler or interpreter version, operating system, hardware details when relevant, and configuration files.
Simulation-specific checks
- Perform a step-size, grid-size, or solver-tolerance study. A stable result should approach a limit as resolution improves, within the stated tolerance.
- Check numerical stability and conservation properties of the algorithm, not just whether it finishes.
- Preserve input data, random seeds or random streams, parameters, intermediate outputs when the system is nondeterministic, and the complete execution environment.
- Compare against an analytic solution, a manufactured solution, a benchmark, or an independently chosen method when one exists.
The National Academies emphasizes clear, specific, and complete descriptions of computational methods and data products so another researcher can rerun the work. A screenshot of a final number is not a reproducible computation.
5. Distinguish reproducibility from replication
Reproducibility means obtaining consistent results from the same inputs, computational steps, methods, code, and analysis conditions. Replication is an independent study that addresses the same question, often with different people, software, data collection, or implementation. A result can be reproducible yet still be wrong because everyone reran the same faulty model; replication tests whether the finding survives an independent approach.
Build a reproducibility package
- Frozen prompt and complete AI response.
- Raw and processed input data with units and provenance.
- Equations, parameter definitions, initial and boundary conditions, and approximation choices.
- Source code, scripts, notebooks, configuration files, and exact execution commands.
- Model, library, compiler or interpreter versions, operating system, hardware, and random seeds where applicable.
- Intermediate outputs needed to diagnose nondeterministic or iterative calculations.
- A readme stating expected outputs, tolerances, and known limitations.
Exact bit-for-bit identity is not always the right requirement. Floating-point arithmetic, parallel execution, stochastic models, and AI systems can produce small differences. Define an acceptable tolerance in advance and justify it from numerical error, measurement uncertainty, or the decision the result supports. NIST describes an analytic result as substantially reproducible when an independent analysis using identical methods produces similar results within acceptable imprecision or error.
6. Quantify uncertainty instead of hiding it in digits
Separate the sources of uncertainty rather than reporting one unexplained percentage.
- Measurement uncertainty: variation and calibration limits in observed inputs.
- Numerical uncertainty: discretization, truncation, round-off, solver tolerance, and convergence error.
- Model uncertainty: error introduced by idealizations, omitted physics, or an equation used outside its validity range.
- Parameter uncertainty: imperfect knowledge of constants, material properties, or fitted coefficients.
- Sampling uncertainty: variation caused by finite samples, Monte Carlo draws, or data selection.
Propagate and report the uncertainty
Use sensitivity analysis to identify which inputs dominate the output. Propagate uncertainties through the actual equations or simulation; do not attach the smallest input error to a result whose model error is much larger. Report the method used, correlations between inputs, and whether the interval represents random variation, a confidence statement, or a coverage convention.
NIST defines standard uncertainty as the estimated standard deviation of a measurement result and denotes a result with its standard uncertainty as y ± u(y). Under the stated normal-distribution conditions, that notation corresponds to approximately 68% coverage. The convention does not automatically apply when the distribution is skewed, bounded, multimodal, or dominated by systematic effects.
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Match significant figures to the evidence
Round only after uncertainty is calculated. Extra decimal places imply precision the inputs and method do not support. If the uncertainty is larger than the claimed effect, report that the effect is unresolved rather than choosing the preferred interpretation. State whether an interval is one standard uncertainty, a wider coverage interval, a tolerance band, or a range from scenario analysis.
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7. Obtain independent scrutiny
Ask a technically qualified reviewer to inspect the setup, not merely proofread the prose. Give the reviewer the frozen claim, equations, assumptions, code, data, uncertainty analysis, and proposed interpretation.
What the reviewer should challenge
- Whether the governing equations and approximations match the physical regime.
- Whether units, vectors, boundary conditions, and conservation laws are handled correctly.
- Whether the implementation matches the written equations and has tests for known cases.
- Whether numerical convergence, sensitivity, and tolerances justify the reported digits.
- Whether uncertainty sources are complete and correctly combined.
- Whether the conclusion claims more than the calculation or measurement establishes.
The U.S. Geological Survey’s Fundamental Science Practices apply reliability, validation, methodological transparency, and rigorous peer review to scientific information, including AI-generated outputs. Review is not a ceremonial final step: it is an independent attempt to find a failure that the original analyst may share with the model.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.8. Label the result according to the evidence
Use a status that states what was checked and what remains unresolved.
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- Partially verified: some checks pass, but a material component—such as model validity, uncertainty, or an independent implementation—remains incomplete.
- Inconsistent: a dimensional, conservation, limiting-case, numerical, or reproducibility check fails, or independent implementations disagree beyond tolerance.
- Unverified: required data, code, method details, or assumptions are missing, so the claim cannot be tested.
Do not call a novel or surprising result established because one AI response produced it. Scientific confidence grows through confirmatory work and cumulative evidence. A transparent “unverified pending data” is stronger than an unsupported assurance.
Hand derivation, simulation, and experiment: what to check
Different forms of evidence fail in different ways. Apply all six axes rather than treating one type as automatically superior.
| Evidence type | Physical validity | Numerical correctness | Reproducibility | Uncertainty and sensitivity | Provenance and disclosure | Independent confirmation |
|---|---|---|---|---|---|---|
| Hand derivation | Check equations, assumptions, and domain of validity. | Check algebra, signs, units, and limiting cases. | Record complete symbolic steps and parameter values. | Analyze sensitivity to measured or assumed parameters. | Preserve the AI output, prompt, edits, and sources. | Use a fresh derivation, symbolic check, or qualified reviewer. |
| Numerical simulation | Check that the encoded model represents the intended physics. | Test stability, convergence, discretization, and implementation. | Share data, code, parameters, dependencies, environment, and intermediate outputs. | Separate numerical, parameter, model, and sampling uncertainty. | Document model/version, settings, seeds, and human oversight. | Compare with an analytic solution, benchmark, or independent method. |
| Experiment | Check apparatus assumptions, calibration, controls, and measured regime. | Check data processing, corrections, and analysis code. | Preserve raw data, protocols, instrument settings, and analysis steps. | Report calibration, random and systematic components, and sensitivity. | Document instruments, dates, operators, AI use, and exclusions. | Seek repeat measurements, an independent lab, or peer review. |
A worked verification pattern
Example: an AI claims a falling object reaches a stated speed
First freeze the exact claim, mass, height, gravitational acceleration, and whether air resistance is neglected. Reconstruct the model: for a drop from rest in a uniform gravitational field with no drag, energy conservation gives mgh = ½mv², so v = √(2gh). The mass cancels; if the AI’s answer depends on mass under these assumptions, investigate.
Check dimensions: gh has units of length squared per time squared, and the square root has units of speed. Check limiting behavior: zero height gives zero speed, and increasing height raises speed as the square root rather than linearly. Compare the predicted speed with the nonrelativistic assumption; if it approaches a regime where that approximation fails, the model must change. Independently calculate the expression, then compare with a time-domain integration of dv/dt = g. Finally, report uncertainty from the height measurement and the adopted value of g, and state that air drag, rotation, and local variations were excluded. This verifies a result only for the declared idealization, not for every real falling object.
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Common failure modes and recovery steps
The answer has no equations or inputs
Classify it as unverified. Ask for the governing law, variables, units, data, assumptions, and computational steps. Do not reverse-engineer a plausible formula from the final number and present it as the model used.
The AI cites a source that does not contain the claimed result
Open the cited source, locate the exact equation or dataset, and compare definitions, units, and conditions. A citation can establish background theory without validating the AI’s particular calculation.
Two runs disagree
Preserve both outputs and compare model version, prompt, settings, random seed, hidden tool calls, and attached files. Re-run with deterministic settings where possible. If the spread is material, treat it as an uncertainty or reproducibility failure until explained; do not select the more convenient answer.
The simulation changes when resolution increases
Perform a convergence study, inspect stability, and determine whether the quantity of interest approaches a limit. If it does not, reduce the claim to the demonstrated resolution or change the numerical method.
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The result is precise but the inputs are not
Recompute with input uncertainty and model uncertainty included. Round the output to the supported precision and explain which uncertainty dominates.
The result violates a conservation or limiting check
Stop before tuning parameters. Recheck units, signs, boundary terms, source terms, and the scope of the conservation law. Then isolate the first failing intermediate calculation with an independent implementation.
A practical verification record
Keep one dated record for each claim. A concise record can contain:
- Claim: the exact output and the conclusion you intend to make.
- Provenance: model/tool, version, prompt, settings, files, date, and human edits.
- Problem definition: equations, symbols, units, geometry, conditions, approximations, and validity domain.
- Checks: dimensions, signs, conservation, limiting cases, scale estimate, and regime test.
- Independent calculation: method, code or algebra, test cases, and comparison tolerance.
- Uncertainty: measurement, numerical, model, parameter, and sampling components, with propagation method.
- Review: reviewer identity or role, challenges raised, responses, and unresolved issues.
- Status: verified, partially verified, inconsistent, or unverified, with the exact assumptions and tolerance attached.
This record lets another person distinguish a valid result from a persuasive story and makes later corrections traceable.
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A defensible conclusion names the scope: “Under the stated equations, inputs, boundary conditions, and approximation, the independent calculation agrees within the declared tolerance; the reported uncertainty is ….” If a required element is absent, say: “The claim remains unverified because the code and parameter definitions are unavailable.” If checks conflict, say which check failed and what would be needed to resolve it. That precision protects readers from both false confidence and blanket distrust: AI can accelerate derivation and coding, but accountability, validation, transparent disclosure, and independent review remain human scientific responsibilities.
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