PISCES: Physics-Informed Solar-wind Convolutional autoEncoder for Space-weather Anomaly Detection and Early Warning

1 Introduction

• About 40 minutes to an hour separates an L1 coronal mass ejection observation from its arrival at the outer magnetosphere, while reliable real-time detection of each transient type remains unresolved.Source: §1 · p. 1
• Amplitude-duration thresholds and jump ratios characterize individual signatures but cannot represent combined magnetic and plasma structures within one transient.The classic intense-storm criterion is southward Bz below −10 nT for more than three hours.Source: §1 · p. 2
• Supervised event-detection methods require labels, while catalogs are incomplete and the reliability of these methods for event types absent from labels is unknown.Potential events with marginal signatures constitute about 10% of the events in the Richardson & Cane catalog.Source: §1 · p. 2
• PISCES trains a convolutional autoencoder on unlabeled solar-wind data using magnetic consistency, temperature–velocity, Parker-spiral, and consecutive-sample change constraints.It reports the magnitude of each constituent physical signature for every flagged window.Source: §1 · p. 2

2 Background

• Supervised solar-wind event methods include labeled ICME segmentation and detection, but reliability for event types absent from labels is unknown and they lack a physical decomposition of flagged windows [7, 8, 10, 11, 12].Source: §2 · p. 3
• Unsupervised autoencoder approaches flag poorly reconstructed segments, while DSOMs classify solar-wind regimes without labels and represent multivariate structure.Source: §2 · p. 3
• Physics-informed losses have been used in PINNs, supervised solar-wind forecasting, and grid anomaly detection, but the authors know of no comparable autoencoder applying a physics loss to in-situ solar-wind data.Source: §2 · p. 3
• PISCES combines unsupervised autoencoder detection, solar-wind physics constraints in its loss, and an anomaly score decomposed into physically interpretable components.Source: §2 · p. 3

3.1 Data and Preprocessing

• Training uses 2005–2015 data, validation uses 2016–2017, and testing uses 2018–2024, with chronological splitting to avoid leakage from recurring or near-duplicate windows.The seven OMNI parameters are divided into 60-minute windows; evaluation and real-time scoring advance one minute at a time.Source: §3.1 · p. 3

3.2 Model Architecture

• The one-dimensional convolutional autoencoder compresses seven channels over 60-minute windows and reconstructs them using a decoder with skip connections at the two upper levels.Its bottleneck contains 40 values, a 10.5:1 compression from 420 inputs; skip dropout is used in training, while inference ordinarily uses full skips.Source: §3.2 · pp. 4–5, Figure 2 · p. 4

3.3 Physics-Informed Loss

• Seven physics losses regularize denormalized reconstructions through magnetic-field consistency, temperature–velocity and Parker-spiral relations, and changes in four derived quantities.The change penalties are empirical regularizers, not claims that transients vary gradually; the temperature–velocity reference is an approximation that varies across wind conditions.Source: §3.3 · pp. 5–7

3.4 Anomaly Scoring

• Each 60-minute window receives 15 sub-scores that combine magnetic and plasma reconstruction errors with physics signatures, raw-input measures, and residual corrections using fixed weights.The physics sub-scores include reconstructed field consistency, entropy, pressure, temperature–velocity, Parker-angle, beta, and dynamic-pressure measures; some additional scores are calculated from raw inputs.Source: §3.4 · p. 8

3.5 Hints of Event Types

• Fixed rules assign event-type hints from magnetic and plasma score fractions and derived physics scores, including thresholds for shocks, magnetic structures, and compression regions.Figure 4 illustrates responses on a synthetic shock-and-ICME profile; its composite trace is illustrative, not model output.Source: §3.5 · p. 8, Figure 4 · p. 9

4.1 Training Specifications

• Training uses a 10-epoch MSE-only warmup, then ramps physics losses over epochs 11–20; early stopping monitors validation MSE with a 25-epoch patience.PISCES-Opto uses a 0.8 skip-dropout probability and reaches validation MSE 0.02196 at epoch 95.Source: §4.1 · p. 10

4.2 Evaluation Methodology

• Detections are compared with DONKI high-speed-stream and shock catalogs and the Richardson & Cane ICME catalog using a ±3-hour match window.ICME positive labels span three hours before catalog start through three hours after catalog end; the 102 catalog intervals from 2018–2024 have a median length of 26 hours.Source: §4.2 · p. 10

4.3 Metrics

• PR-AUC, computed as average precision, is the primary metric because ICME interval labels produce a positive-window frequency of about 11.9%.The evaluation also reports window- and event-level detection, false-alarm, skill, precision, and detection-offset measures.Source: §4.3 · p. 10

5.1 Performance Comparison

• At the 99th-percentile threshold, PISCES-Opto matches 194 of 848 eligible catalog events, with mean and median onset offsets of −133.5 and −66.5 minutes.Only 29.4% of matched detections precede catalog onset, so these offsets are not warning lead times.Source: §5.1 · p. 11, Table 1 · p. 12
• PISCES-Opto's selected run reaches PR-AUC 0.365, the highest among eleven runs, but the checkpoint was selected after corrected test metrics were inspected.The window energy score reaches PR-AUC 0.341 and exceeds six of the seven method rows above it.Source: Table 1 · p. 12, §5.1 · p. 14
• High-speed-stream detections are less frequent in part because their gradual, multi-day regions are approximated by ±3-hour point labels.At 1 AU, these regions change gradually over about 60 minutes, unlike abrupt shock boundaries.Source: §5.1 · p. 12
• Event POD is 0.690 for ICMEs, 0.248 for interplanetary shocks, and 0.107 for high-speed streams, but unequal label exposure confounds this ordering.Effective positive-label exposure is 26.2 hours per ICME, 4.9 per shock, and 5.0 per stream; the comparison does not isolate event physics, label duration, or overlap.Source: §5.1 · pp. 12–13, Table 2 · p. 14

5.2 Ablation with Physics Loss Groups

• Across five matched runs, mean average precision is 0.291 for Varµ, 0.300 for Varγ, 0.309 for Varθ, and 0.294 for VarΣ, with no stable ordering across seeds.The best-to-worst mean gap is 0.018, smaller than the within-group ranges; the results do not attribute differences to particular physics terms.Source: §5.2 · p. 16, Table 3 · p. 16
• Mean average precision is 0.304 for the seven-constraint objective, 0.263 for the derived-quantity objective, and 0.257 for reconstruction alone, but three runs do not establish superiority.The selected PISCES-Opto checkpoint was chosen after corrected test scores were inspected.Source: §5.2 · p. 16
• None of the group or objective means exceeds the no-model references: 0.337 for an untrained network and 0.341 for window energy.Four individual trained runs exceed those references, but the pattern is not consistent; the results support using sub-scores to describe physical changes and hint at event types.Source: §5.2 · p. 16

Kendall Uncertainty Weighting Failure

• Uncertainty weighting degenerates when change penalties approach zero, driving log-variance weights toward −∞ and degrading MSE; the study therefore uses fixed weights.The failure occurs when the weighting objective is applied to a loss that can approach zero.Source: Kendall Uncertainty Weighting Failure · p. 17

5.3 Skip Path Attenuation

• Zeroing skip contributions at inference raises test average precision from 0.365 to 0.406, while window metrics improve and event POD falls from 0.229 to 0.154.The intervention worsens reconstructions throughout the test set; attenuation selected on validation improves window ranking but reduces event coverage.Source: §5.3 · pp. 17–18
• Retraining without skip connections yields average precision of 0.227 to 0.230, below trained models with full or attenuated skips, but the comparison does not isolate the cause.Skipless retraining also removes feature-fusion parameters, reducing the parameter count from 12,555 to 11,571.Source: §5.3 · p. 18

5.4 An Untrained Network

• With full skips, untrained runs average 0.337 ± 0.005 average precision versus 0.306 ± 0.029 for trained runs, but the difference is marginal and lineage-sensitive.The untrained group has the higher mean at p = 0.054; a restricted homogeneous trained subset instead scores 0.031 below the untrained mean at p = 0.008, which does not resolve the full comparison.Source: §5.4 · p. 18
• Attenuation raises trained-run average precision by +0.070 ± 0.028, while untrained runs gain only +0.0001 ± 0.0003 and show little evidence for a preferred scale.Validation scores across four scales change by at most 6.4 × 10−4 for untrained runs.Source: §5.4 · pp. 18–19, §5.3 · p. 18
• With validation-selected attenuation, the eleven trained runs reach 0.376 ± 0.020 average precision, exceeding both the untrained mean and the tuned tree baseline at 0.373.The comparison against untrained runs has exact permutation p = 0.004.Source: §5.4 · p. 19, Table 5 · p. 19
• Physics-trained runs without physics terms have mean pairwise component-ranking correlation 0.937, versus 0.242 with untrained runs; physics terms alone do not explain the ordering.Runs trained with different objectives give similar component rankings.Source: §5.4 · p. 19

5.5 Trailing Median Smoothing and Estimated Warning Leads

• Warning analysis uses trailing rather than centered 15-minute median smoothing, so each output uses current and preceding scores only; average precision changes by at most 0.003 across the reported runs.The 99th-percentile threshold is derived from validation scores after the trailing filter.Source: §5.5 · pp. 19, 22
• Subtracting the L1-to-bow-shock delay from OMNI timestamps estimates the associated L1 observation time, but does not establish input availability or operational alert latency.Shock timing uses a further propagation correction; for 80 abrupt-onset shocks, measured L1-to-ground delay has a median of 46 minutes.Source: §5.5 · pp. 19–20
• Across three runs, full skips cover 29 to 35% of eligible sudden commencements with median estimated leads of 24 to 28 minutes, versus 18 to 20% and 18 to 19 minutes with validation-selected attenuation.Attenuation has higher average precision, while full skips associate more events with alarms; the ranges are descriptive, not paired treatment effects.Source: §5.5 · pp. 20, 22, Table 6 · p. 21, Figure 10 · p. 23
• Trained runs match more sudden commencements than untrained runs, but the interpretation changes after normalizing by alarm episodes, and shock coverage reverses direction.The sudden-commencement match rate per episode is 14% higher for trained runs, while every trained run has fewer anchored-shock matches per episode than every untrained run.Source: §5.5 · pp. 20–21
• At P95, full skips associate 78 of 112 sudden commencements (70%) with a median estimated lead of +35 minutes at 5.7% duty cycle.At P99.5, full skips still associate 27 of 112 events at 0.8% duty cycle; Figure 9 sweeps thresholds from P95 to P99.5.Source: §5.5 · p. 21, Figure 9 · p. 22
• On the exact overlap of 948,623 timestamps, raw ACE average precision is 0.415 and 0.462, compared with 0.369 and 0.434 for smoothed OMNI scores.The differences are +0.045 and +0.028; shifting OMNI timestamps changes the paired set, so the comparisons do not isolate timestamp alignment from coverage.Source: §5.5 · p. 22

5.6 Cross Validation Across Solar Cycle Phases

• The design splits 2005–2024 into sequential one-, two-, or four-rotation blocks, leaves one rotation around each test block unused, and retrains on the remaining data.Of 460 folds, 80 are omitted because they contain no retained catalog event; the split review found earlier alternatives unusable or potentially duplicative.Source: §5.6 · p. 23
• Across 380 valid folds, PR-AUC averages 0.265, 0.273, and 0.264 for blocks of one, two, and four solar rotations, while one-rotation blocks average 0.35 near the cycle 24 maximum and 0.12 near the 2019–2020 minimum.The comparison with the eleven-run mean of 0.306 ± 0.029 does not separate training composition, short-block evaluation, or run variation.Source: §5.6 · p. 23
• Corrected fold results supersede an earlier mean of 0.376, which used physics weight 0.2 despite being labeled pw30 and followed an earlier scoring setup.The paper distinguishes cross-validation across cycle phases from chronological holdout on an unseen future.Source: §5.6 · p. 23

5.7 Score Decomposition Analysis

• The Gannon superstorm figures show shock, sheath, ejecta, and recovery structure, while the heliospheric map is qualitative and does not establish exact magnetic connectivity.Hodograms contrast coherent ICME flux-rope rotation arcs with abrupt component turns in interplanetary shocks.Source: §5.7 · p. 24
• Table 7 reports mean and maximum sub-scores over 2,969,144 PISCES-Mono test windows; reconstruction terms have unit weights and physical or derived terms have weights from 0.002 to 0.005.The Bt consistency residual has the largest maximum-to-mean ratio, though its numerical scale depends on its units and definition.Source: §5.7 · p. 24, Table 7 · p. 24

• For the Gannon storm, total pressure peaks near 2 nPa, about 256 times its pre-storm median, while the Alfvén Mach number reaches a minimum near 1.2.Source: §5.8 · p. 26
• Event-type sub-score patterns are descriptive because peak-composite window selection can bias components, and only total pressure jump survives neither Bonferroni correction nor the small event sample caveat.Source: §5.8 · p. 32
• Peak-window selection bias depends on sub-score correlation with the composite; median aggregation removes the tested maximum-selection effect but not other possible biases.Source: §5.8 · p. 34
• Trained runs show more consistent sub-score rankings than untrained runs, with mean Spearman ρ of 0.88 versus 0.53; the trained–untrained correlation is 0.28.Source: §5.8 · p. 34
• The ranking consistency is associated with trained weights, not physics terms alone: physics-free trained runs correlate 0.913 with physics-trained runs, near their within-group 0.937.Source: §5.8 · p. 34
• The fixed sub-score rule classifies only 80 of 194 alarmed events correctly, barely exceeding the majority-class rule’s 79.Source: §5.8 · p. 35
• Removing all physics terms from training lowers average precision from 0.304 to 0.217, while removing the terms only from scoring changes it by 0.029 when training includes them.Source: §5.8 · p. 35

Contributions of Decomposition

• PISCES decomposes scores into physical components, but does not establish higher aggregate detection performance or map those variables reliably to event classes.Source: Contributions of Decomposition · p. 35

Effects of Training

• Validation-selected skip attenuation raises trained-run average precision by 0.070 ± 0.028 on average, while untrained-run average precision changes by only 0.0001 ± 0.0003.The attenuation analysis was designed after inspecting test results, and the comparison does not isolate the mechanism.Source: Effects of Training · pp. 35–36

From Detection to Early Warning

• Trailing-median alarms match sudden commencements with median estimated leads of 23.9 to 27.9 minutes for trained runs, but event subsets differ and the analysis does not establish a paired timing effect.Source: From Detection to Early Warning · p. 36

Limitations

• Baseline comparisons favor PISCES because its configurations were tuned more extensively; training and test periods also differ in spacecraft sources and data coverage.OMNI timestamps are shifted to predicted bow-shock arrival, so they do not establish observation, receipt, or alert times.Source: Limitations · pp. 36–37

Future Work

• Future evaluation calls for prospective live-data records processed in receipt order, a blind period with a preregistered analysis, and randomized forecaster comparison of decomposed and single scores.Source: Future Work · p. 37

• PISCES-Opto reaches average precision of 0.365 across pooled 2018–2024 score windows, with a calendar-month bootstrap 95% confidence interval of 0.306 to 0.419.The checkpoint was selected after corrected test-metric inspection, so this is retrospective rather than blind-test evidence.Source: §7 · p. 37
• Skip attenuation raises mean average precision across eleven runs from 0.306 ± 0.029 to 0.376 ± 0.020, but the analysis was designed after test inspection.Source: §7 · p. 37
• Trailing-median alarms matched 20 to 22 sudden commencements with attenuation versus 32 to 39 with full skips, but the differing matched-event subsets do not establish a paired effect.Source: §7 · p. 38
• Operational testing needs live DSCOVR and ACE data processed in receipt order, with observation, receipt, and alert times recorded, plus blind evaluation and forecaster studies.Source: §7 · p. 38

• Window counts in the split summary exclude windows that still contain missing values after preprocessing.Source: Table 8 · p. 43
• Training and early-stopping validation advance 60-minute windows by 15 minutes.Source: Table 8 · p. 43
• Test evaluation and validation-threshold estimation advance 60-minute windows by one minute.Source: Table 8 · p. 43

B Physics Constants

• Physics-loss constants are expressed in OMNI units: nT, cm−3, K, km/s, and nPa.Source: Table 9 · p. 43
• The listed SI values are kB = 1.38065 × 10−23 J/K and µ0 = 4π × 10−7 H/m.Source: Table 9 · p. 43
• The Alfvén-speed factor is the only listed constant not used in training loss; it enters only the Alfvén Mach score.Source: Table 9 · p. 43

C Hyperparameters

• Table 10 combines values from the saved checkpoint and training configuration with remaining values taken from the training scripts.Source: Table 10 · p. 44
• Listed settings include seven loss coefficients, pwmax, warmup and ramp periods, encoder filters, decoder kernels, skip dropout, learning rate, patience, and parameter count.Source: Table 10 · p. 44
• The squeeze-and-excitation reduction ratio is 4, giving hidden widths of 8, 4, and 4 for channel counts 32, 16, and 8.Source: Table 10 · p. 44

D Sensitivity to Matching Tolerance

• Window POD falls from 0.079 to 0.045 because positively labeled windows grow faster than true-positive alarm windows.Source: D Sensitivity to Matching Tolerance · p. 45
• At 3 hours, PR-AUC is 0.322, matching PISCES-Mono in Table 1; changing tolerance alters labels and hit assignments, not timestamps.Source: D Sensitivity to Matching Tolerance · p. 45
• Detected events rise from 61 to 201 of 848, PR-AUC from 0.220 to 0.419, and FAR falls from 0.557 to 0.188 as tolerance widens.Source: Table 11 · p. 45, D Sensitivity to Matching Tolerance · p. 45
• PR-AUC depends on tolerance-defined event labels rather than alarm threshold, while POD and FAR use the 99th-percentile validation threshold.Source: Table 11 · p. 45