Deep Learning Meets ETAS¶

Francisco Plaza-Vega · STATSEI14 · 13 October 2026

From seismic research to one small experiment¶

How can we represent seismic history so that a model can learn something useful about what follows?

The presentation approaches this question through the published Spatial Statistics study and the aftershock work developed through Isidora Jara's thesis and the subsequent manuscript. They use different representations and targets: ETAS-derived intensity summaries and the macrozone of their maximum in the first study; aftershock sequence representations, predictive tasks and generative modelling in the later work. Their results do not measure the task in this notebook. An ETAS–GAN combination remains a research proposal; it has no empirical implementation in this tutorial or the manuscript discussed here.

Here we make the question small enough to investigate together: use 30 days of regional catalogue history to estimate the probability of at least one M ≥ 5 catalogue event in the next seven days. We compare a learned sequence representation with simple baselines, then ask whether an additional channel inspired by magnitude and temporal decay helps.

The same thread runs through every step: question → representation → model and loss → evidence. We will build windows, train a small Keras LSTM and interpret a controlled comparison. Every learning step remains visible in Python.

Our 23-minute guided practical: setup (25–28), windows and splits (28–32), baselines and LSTM (32–38), add a channel (38–43), and evaluation (43–48), using minutes from the start of the session. A separate Transformer demonstration follows at 48–56, with closing discussion at 56–60. Open transformer-demo.ipynb for that comparison, or follow its prepared solution. You can participate by running cells or by interpreting the supplied results.

Scope: the frozen USGS catalogue contains revised versions downloaded in 2026. Event-time separation below does not reconstruct historical information availability. This is a retrospective teaching experiment, not an operational forecast or a prediction of shaking or risk.

Run cells in order. Use training and validation for the exercise; run the final test after fixing your configuration.

1. Environment and files¶

Use a CPU runtime. Locally, extract the course pack and open this notebook inside it. In Colab, upload the supplied data-pack.zip when prompted. The setup never silently downloads a changing catalogue.

If imports fail, run this in a separate cell and restart:

%pip install tensorflow==2.19.1 pandas scikit-learn matplotlib

The full tested versions are in requirements.txt. The recorded local CPU timing is not a Colab guarantee.

2. Inspect the frozen catalogue¶

The download starts at M=3 for coverage diagnostics. Inputs use M≥4.5; the target includes events exactly at M=5. Catalogue magnitude is not uniformly Mw.

Review coverage and magnitude types before changing region. A magnitude-frequency plot alone cannot certify completeness. Parameter choices are predeclared; test metrics do not select them.

3. One origin, one history, one target¶

Our first modelling choice is the representation. We summarize a regional catalogue as daily channels and predict weekly occurrence; we are not reconstructing individual events or the spatial intensity field used in the research presentation.

Each Monday at 00:00 UTC defines an example. Input: [origin − 30 days, origin). Target: [origin, origin + 7 days). Adjacent targets do not overlap; seismic dependence can remain.

Each day has log event count, maximum magnitude above the input threshold, and an occupancy indicator. An empty day has zero excess and zero occupancy. Point to one history and its target before running the cell: which details of the original catalogue have these summaries retained, and which have they discarded?

The fourth channel sums 10**(alpha*(m-M0)) * (1+age_days/c)**(-p) at each day's end, using only past events inside the same input history. Larger and more recent events receive larger contributions. It is an ETAS-inspired index, with illustrative parameters, no spatial kernel and no fitted rate. We construct it now and add it to the LSTM in Section 7.

4. Chronological split and label purging¶

Past input may reach into a preceding partition. A future target cannot cross the next boundary. Weeks without a complete target are dropped. Class counts describe the sample; they do not determine test-driven changes.

Normalization learns its mean and scale from training inputs only. These controls concern event time, not historical reporting or revision availability.

5. Simple baselines¶

Before asking whether a flexible sequence model helps, establish what simple summaries can achieve. The constant forecast uses training prevalence. Logistic regression receives mean, maximum and final-day summaries of each channel. Its scaler also uses training only.

Comparing each model with and without the score helps distinguish the contribution of this added representation from the choice of architecture. Logistic regression and LSTM do not receive identical representations: one sees summaries, the other an ordered daily sequence.

6. A small Keras LSTM¶

Return to the presentation's sequence model: the LSTM transforms the 30 daily inputs into a learned representation. A sigmoid output and binary cross-entropy connect that representation to our weekly occurrence question. Choosing an LSTM does not itself determine the scientific target.

Sequential stacks layers. Input describes one example's shape. LSTM(16) learns a sequence representation; Dense(1, sigmoid) produces one probability. compile chooses the optimizer and binary cross-entropy loss.

fit updates weights using training examples. An epoch passes through training data; a batch contains up to 64 examples. The callback stops after validation loss fails to improve for three epochs and restores the best weights. Validation does not update weights by backpropagation.

7. Required exercise: add the ETAS-inspired channel¶

Before changing the model: write one sentence predicting whether this channel will help, and why. Its magnitude weighting and temporal decay provide a structured summary of recent activity. The existing channels may already contain enough information, or the illustrative score may be poorly suited to this target.

Add "log_etas_score" to exercise_feature_names, then rerun selection, model, fit and validation. Keep splits, seed and hyperparameters fixed. The solved notebook already contains this change.

After the comparison: record validation Brier score and log loss before and after. Was your expectation supported in this run? Does the channel also help logistic regression? Describe what changed in the representation and what remained fixed in the forecasting question.

Neutral or worse results are useful evidence. One seed and region cannot establish universal superiority. Both LSTMs share their architecture and protocol, but an additional channel adds some input weights. This experiment adds a feature; it does not fit ETAS or implement an ETAS–GAN model.

Homework extension: 14 versus 30 days¶

Keep the live session focused on the channel comparison. Afterwards, copy the notebook, set LOOKBACK = 14 in the configuration cell, and rebuild windows, splits, normalization and models. Compare validation only. The score must use the same shorter history. Keep the seven-day target fixed. Follow the homework guide for further experiments and reporting prompts.

8. Final test evaluation¶

The model families and protocol are fixed above. Run the next cells once after fixing the exercise configuration. Do not choose new settings from test metrics and then call that test untouched. The homework continues on training and validation; this already inspected test period cannot become an untouched test for a newly selected model.

Brier score is squared probability error; log loss penalizes confidently wrong forecasts. Smaller is better. Calibration compares mean probabilities and observed frequencies; bin counts matter.

9. Save an auditable run¶

The solution writes results/reference-run; the participant notebook writes results/participant-run. The website reads prepared artifacts and never trains models. Saved predictions, raw features, configuration, hash and timings support inspection. Seeded runs can differ slightly across TensorFlow builds.

10. Return to the scientific question¶

Use the evaluation block at minutes 43–48 to connect this experiment back to the research, then carry these questions into the Transformer demonstration and the final discussion at 56–60: what did we choose to represent, what did we ask the model to learn, and what evidence did we obtain?

1. Did the ETAS-inspired score support your initial hypothesis on validation? Did the observed difference persist in the reserved test period?
2. Did the channel help logistic regression and LSTM equally? What does that suggest about this representation, within the limits of one run?
3. What did daily regional summaries discard about locations, individual magnitudes and within-day event timing? How would the question change if the output were an intensity summary or an aftershock sequence?
4. How many weeks support each calibration bin? What could temporal dependence do to uncertainty?
5. What would change if completeness, reporting delays or magnitude types changed?

Take-away: deep learning offers flexible ways to connect a representation to a specified task. Scientific usefulness depends on that choice and on evidence against appropriate baselines. A more flexible model need not win this comparison.

Limits: revised catalogue, one region, one seed, dependent weeks, limited positive examples and illustrative parameters. Strict operational replay needs archived versions and availability times for inputs and training labels.

The closing architecture comparison¶

The separate transformer-demo.ipynb keeps the catalogue-only representation and target fixed while comparing LSTM and attention across three seeds. Its prepared pilot results belong to a different run from this one-seed feature exercise. Discuss the measured losses and then propose an explanation that a new experiment could test. A difference in score alone cannot identify whether sample size, representation, target or training choices caused it.

Continue after the session¶

The homework guide develops the representation and modelling questions further. Keep a copy of this fixed run, state your hypothesis before each change, and work on training and validation when choosing new settings.

Prepared-results fallback¶

If training fails, stop the live training cells. Open the supplied workshop-solved.html and results/reference-run/{metrics,predictions}.csv, plus runtime.json. Those outputs identify a separate prepared run, not successful training on your machine.

Optional new USGS download¶

Keep the frozen file for the workshop. For a separate experiment, use python scripts/prepare_data.py --refresh from the course source folder, or query the USGS API. A new region or vintage requires new provenance, an intentional checksum update and fresh checks. The current box cannot supply events outside its boundaries.

Keras LSTM · Nicolis, Plaza & Salas (2021)

The published ETAS/LSTM/CNN study and the aftershock generative manuscript under review use different targets. Their scores are not results for this notebook. ETAS–GAN remains a proposed extension outside the empirical scope of both this practical and the manuscript.