The Force of a Prediction: Transferability, Stability and Uncertainty in Learned Atomic Potentials Codex (AI) | Commissioned review v1 | 2026-10-22 A learned interatomic potential must do more than interpolate energies on a held-out dataset. Forces, conservation, long trajectories and unfamiliar configurations determine whether it can support scientific simulation. This review connects local neural and equivariant models with a controlled potential-error example, showing why low energy error need not imply accurate dynamics. A potential is a dynamical model An interatomic model maps configurations to energy and, through derivatives or direct prediction, to forces. Those forces determine trajectories and sampled thermodynamic states. A small average error on isolated configurations can coexist with large errors in rare regions that control barriers or stability. Evaluation must follow the intended simulation rather than stop at a static benchmark. Representation advances Behler and Parrinello introduced a general neural-network representation of high-dimensional potential-energy surfaces. Batzner and colleagues developed E(3)-equivariant graph neural networks for interatomic potentials. Musaelian and colleagues extended local equivariant representations for large-scale atomistic dynamics. These advances improve representation and efficiency, while leaving transfer and long-time validation as separate scientific requirements. References: ef-34-1, ef-34-2, ef-34-3 Symmetry is necessary structure Translation, rotation and permutation symmetries constrain physically meaningful predictions. Encoding them can reduce the amount of data needed and prevent some inconsistent outputs. Symmetry alone, however, does not specify the correct potential surface. Many wrong models obey the same invariances, so architectural compliance cannot replace validation against independent configurations and observables. Derivatives amplify small structure A small-amplitude oscillation in predicted energy can have a large derivative if it varies rapidly with position. Energy error and force error therefore probe different properties. A model with smooth-looking energy statistics may still generate noisy forces. Training and evaluation should inspect both, with units and normalization explicitly stated. Locality is an approximation A finite neighborhood representation assumes that more distant effects are either negligible or handled separately. Long-range electrostatics, collective polarization and changes in charge state can challenge that assumption. A local model can work well within one regime while failing when system size or environment changes. The validity domain should be demonstrated rather than inferred from architectural elegance. Random splits can be too easy Nearby frames from one trajectory are correlated. Randomly assigning them to training and test sets can test interpolation between almost identical configurations. Holding out entire trajectories, thermodynamic conditions or structural families provides a stronger transfer assessment. The split should reflect the deployment question, not merely produce a convenient large test count. Dynamics creates its own distribution A model's trajectory can visit configurations absent from the reference dataset. Small errors can then feed back into further exploration of unfamiliar states. Stability over a short run is useful but does not prove correct equilibrium sampling or reaction kinetics. Independent structural, thermodynamic and transport observables are needed. Uncertainty should guide validation An ensemble of models can identify disagreement, but shared training data and architecture can make them confidently wrong together. Uncertainty estimates should be calibrated against independently obtained reference calculations. A useful active-learning loop records which configurations triggered acquisition and tests whether those additions improve the intended physical observable. Trajectory stability is an observable consequence Small average force error on a static test set does not guarantee a stable long trajectory. Repeated integration can visit configurations absent from training, and a potential can contain unphysical low-energy regions that attract the dynamics. A proposed validation would test energy conservation under appropriate integrators, equilibrium distributions and known limiting configurations, while recording when the model leaves its supported domain. These tests should use configurations independent of the fitting trajectory. A model that remains numerically stable can still predict the wrong physics, so stability and fidelity need separate endpoints. Uncertainty estimates need failure examples An ensemble can agree because its members share architecture, data and blind spots. Low disagreement is therefore not sufficient evidence that an unfamiliar configuration is safe to simulate. A proposed calibration would include deliberately shifted chemistries, temperatures or coordination environments and compare uncertainty with observed force and energy errors. The policy for requesting a new reference calculation should be evaluated on those shifts. The oscillatory-energy example shows why derivative behavior deserves direct testing: equal energy-error amplitude can conceal very different force error. A useful uncertainty mechanism should respond to the quantity that drives the downstream simulation. A model that can be challenged The four equations below are a compact analytical model, not a joint fit to all the cited papers. Their interpretation is as follows. A local energy decomposition sums environment-dependent contributions; long-range effects require justification or additional terms. Energy-derived forces preserve conservative structure when derivatives are computed consistently. A small energy perturbation can produce a large force perturbation at high spatial frequency k. Energy drift is one diagnostic in an isolated conservative simulation; thermostats and integrator error must be distinguished from model error. The observational target is forces, trajectory stability and independent physical observables. The model deliberately isolates a tractable mechanism; its purpose is to reveal which measurements would distinguish that mechanism from an alternative. Parameter values in the figures are declared illustrative inputs. A curve produced by those values is a mathematical consequence, not an estimate of an unmeasured biological or physical quantity. A discriminating validation design The primary comparison should test physical-observable accuracy beyond random-frame interpolation. The unit of independent replication is independent trajectory or structural family; repeated readings from the same unit improve precision but do not create independent replication. A strong validation would hold out new thermodynamic states and chemical environments before choosing thresholds or fitting nuisance corrections. In particular, unseen configurations and omitted long-range interactions must be measured, constrained or varied in a sensitivity analysis. Report both the principal estimate and how it changes when that assumption is relaxed. A model that succeeds only after choosing the most favorable exclusion rule has answered a different question from one evaluated with a locked rule. Worked numerical analysis In a dimensionless example with energy-error amplitude epsilon = 0.01, increasing spatial frequency k from one to 100 leaves the maximum energy error unchanged but raises maximum force error from 0.01 to one. A separate calculation compares random-frame and condition-level evaluation conceptually through their sampling units; no benchmark score is invented. The first plot shows energy perturbations at frequencies one and ten; the second plots the peak derivative-error amplitude as frequency increases to 100. These calculations can be reconstructed from the companion Python file and its parameter table. Axis labels retain the model's units, and the caption distinguishes the quantities varied from those held fixed. The numerical examples were selected to expose a dependency, not to reproduce the appearance of a published figure. A useful independent check is to evaluate a limiting case and then recompute an intermediate point without the plotting code. Agreement validates the arithmetic within the declared model; it does not establish that nature follows that model. Evidence, transfer and next steps The scope of the conclusion is limited by unseen configurations and omitted long-range interactions. Transfer to new thermodynamic states and chemical environments requires evidence beyond fitting the original observations. A future replication should preserve raw measurements, calibration records, exclusions and a machine-readable link between each result and the corresponding analysis. The evidence table below identifies what each selected primary study contributes. The comparison is a focused narrative synthesis, not a systematic review or a claim that all subsequent evidence has been surveyed. The proposed study has not been performed here. Its value is that a negative result would constrain an explicit explanation rather than merely lower a benchmark score. Equations (1) E_\theta=\sum_i\varepsilon_\theta(\mathcal N_i) A local energy decomposition sums environment-dependent contributions; long-range effects require justification or additional terms. (2) \mathbf F_i=-\nabla_i E_\theta Energy-derived forces preserve conservative structure when derivatives are computed consistently. (3) \delta E(x)=\epsilon\sin(kx),\quad\delta F(x)=-\epsilon k\cos(kx) A small energy perturbation can produce a large force perturbation at high spatial frequency k. (4) \Delta E_{drift}=E(t)-E(0) Energy drift is one diagnostic in an isolated conservative simulation; thermostats and integrator error must be distinguished from model error. Analytical figures Figure 1. A small energy error can oscillate rapidly Both displayed energy perturbations have amplitude 0.01. Frequencies are expressed per coordinate unit; these are analytic functions, not errors measured from a trained potential. figures/atomistic-potential-transfer-01.csv Figure 2. Equal energy error can hide unequal force error Differentiating an energy perturbation 0.01 sin(kx) gives force-error amplitude 0.01k. Increasing frequency from 1 to 100 raises the peak force error from 0.01 to 1 without changing peak energy error. figures/atomistic-potential-transfer-02.csv Comparison Evidence or design choice | What it identifies | What remains unresolved Source 1 | Neural potential-energy representations enabled high-dimensional atomistic modeling. | Representation does not establish transfer to arbitrary chemistry. Source 2 | E(3)-equivariant networks improved data-efficient interatomic prediction. | Symmetry compliance is not sufficient evidence of correct dynamics. Source 3 | Local equivariant models supported large-scale atomistic dynamics. | Locality and training coverage bound the validated regime. Primary observable | forces, trajectory stability and independent physical observables | unseen configurations and omitted long-range interactions Independent test | physical-observable accuracy beyond random-frame interpolation | Requires new measurements Transfer set | new thermodynamic states and chemical environments | Not validated by the constructed numerical example Proposed validation protocol 1. Specify forces, trajectory stability and independent physical observables before fitting. 2. Retain independent identifiers for each independent trajectory or structural family. 3. Separate new thermodynamic states and chemical environments from model development. 4. Measure or bound unseen configurations and omitted long-range interactions. 5. Record units, calibration and the observation operator. 6. Compare the primary model with a named rival explanation. 7. Prespecify the test: physical-observable accuracy beyond random-frame interpolation. 8. Archive raw data, exclusions, parameter files and executable analysis. Limitations 1. Representation does not establish transfer to arbitrary chemistry. 2. Symmetry compliance is not sufficient evidence of correct dynamics. 3. Locality and training coverage bound the validated regime. 4. Companion figures are constructed analytical examples, not new experimental results. 5. Transfer to new thermodynamic states and chemical environments has not been demonstrated by this review. Research questions 1. Which rare configurations control the intended physical observable? 2. When does a local representation fail under size or charge changes? 3. How can uncertainty be calibrated against genuinely independent reference calculations? Source evidence ef-34-1: Neural potential-energy representations enabled high-dimensional atomistic modeling. Boundary: Representation does not establish transfer to arbitrary chemistry. Locator: Abstract / selected primary-source sections; see linked bibliographic record. ef-34-2: E(3)-equivariant networks improved data-efficient interatomic prediction. Boundary: Symmetry compliance is not sufficient evidence of correct dynamics. Locator: Abstract / selected primary-source sections; see linked bibliographic record. ef-34-3: Local equivariant models supported large-scale atomistic dynamics. Boundary: Locality and training coverage bound the validated regime. Locator: Abstract / selected primary-source sections; see linked bibliographic record. References ef-34-1. Jörg Behler, Michele Parrinello. Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces. Physical Review Letters (2007). https://doi.org/10.1103/physrevlett.98.146401 ef-34-2. Simon Batzner, Albert Musaelian, Lixin Sun, Mario Geiger, Jonathan P. Mailoa, Mordechai Kornbluth, Nicola Molinari, Tess E. Smidt, Boris Kozinsky. E(3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials. Nature Communications (2022). https://doi.org/10.1038/s41467-022-29939-5 ef-34-3. Albert Musaelian, Simon Batzner, Anders Johansson, Lixin Sun, Cameron J. Owen, Mordechai Kornbluth, Boris Kozinsky. Learning local equivariant representations for large-scale atomistic dynamics. Nature Communications (2023). https://doi.org/10.1038/s41467-023-36329-y Provenance A focused narrative analysis of the named primary studies, not a systematic literature search or a claim to comprehensive coverage through 2026. Source-based research review and original mathematical analysis written by Codex (AI). Cited experiments belong to the cited research teams. Concept cover created with the built-in ImageGen tool. Quantitative figures are explicit constructed analyses, with code and numerical data; they are not measurements from the cited papers. This local draft has no independent peer-review or journal-acceptance record.