Cross-Market Meta-Learning for Electricity Price Forecasting

AI summary

Overview

Research area: Machine learning for energy systems — specifically day-ahead electricity price forecasting, meta-learning, and graph-aware sequence modeling.

Technical level: Advanced. The paper assumes familiarity with transformer architectures, MAML-style meta-learning, quantile (pinball) loss, and locational marginal price market structure.

Scope: The paper proposes MetaGrid, a topology-aware, zone-count-independent transformer that is meta-trained across five U.S. ISO markets and then adapted to a held-out grid it has never seen.

What This Paper Is About

Day-ahead electricity price forecasting is normally done one market at a time: a separate model is fitted to each grid's own history, and each pricing zone is treated as an isolated time series. This caps accuracy, because a single ISO offers only a few years of hourly prices — enough to saturate gradient-boosted trees but not enough to train high-capacity sequence models — and because it throws away the spatial dependencies created by grid topology and congestion. The paper's goal is to treat the operating histories of established ISOs as a pretraining corpus and meta-train a single parameter set, independent of zone count, that adapts quickly to an unseen grid.

Key Contributions

1. A five-market benchmark with leakage-free evaluation. Five U.S. ISOs (CAISO, ERCOT, MISO, NYISO, PJM) are scored with identical chronological splits and identical inputs — trailing prices, day-ahead load forecasts, and calendar features — against ten diverse baselines, with results averaged over five seeds.

2. MetaGrid, a meta-trained topology-aware transformer. Every parameter is independent of zone count: no learned zone identities are used, the patch projection, transformer weights, cross-zone attention, and quantile head are shared across all zones and ISOs, so one initialization applies to an unseen grid of any size.

3. Evidence that cross-market transfer improves accuracy on an unseen grid. On every held-out ISO, pretraining beats target-only training of the same architecture; the meta-objective itself is also shown to contribute beyond pooled pretraining.

4. A soft, learned structural prior. Grid adjacency and context correlation enter cross-zone attention as additive, bounded biases whose learned weights differ by market — NYISO relies more on adjacency (α = 0.71) while MISO leans on correlation (β = 0.54).

Main Findings

• Best average point and probabilistic accuracy: MetaGrid attains the lowest average MAE and AQL of the comparison, at 8.032 ± 0.028 $/MWh and 3.263 ± 0.002, improving on the strongest baseline by 3.1% MAE and 3.5% average quantile loss.

• Transfer beats scratch training: The same architecture trained from scratch averages 8.699 ± 0.062 MAE and 3.652 ± 0.005 AQL, so pretraining improves MAE by 7.7%.

• Smaller than competing neural models: MetaGrid uses 7.8M parameters, within 2x of PatchTST and roughly 90x smaller than Chronos-T5-large, yet outperforms both on average.

• Per-ISO results: MetaGrid records 9.04 ± 0.009 (PJM), 8.78 ± 0.06 (NYISO), 5.64 ± 0.06 (CAISO), 6.43 ± 0.005 (MISO), and 10.27 ± 0.004 (ERCOT) $/MWh. It wins on 4 out of 5 ISOs.

• ERCOT is the exception: TSFM baselines outperform MetaGrid there; Chronos T5-large posts the best single-market ERCOT result at 9.77 ± 0.009 $/MWh.

• Zero-shot transfer is partly competitive: MISO reaches $6.43/MWh without seeing MISO prices during training, though pretraining is most effective when combined with adaptation.

• Graph module matters: Removing the graph-aware cross-zone module raises MAE by 0.39 $/MWh, to 8.42 ± 0.007, degrading performance on all five ISOs.

• The meta-objective adds value beyond pooled pretraining: Replacing it with ordinary pooled pretraining over the same four source markets costs 0.29 $/MWh (8.32 ± .02 average), while removing cross-market pretraining altogether costs 0.67 $/MWh (8.70 ± .06 average).

• Learned priors are stable across initializations: Starting α and β from 0.036 versus 1.000 produces nearly the same learned values on every market, indicating the weights are learned from data rather than inherited from initialization.

• Documented failure modes: MetaGrid loses on ERCOT, adaptation degrades MISO, and price spikes are underpredicted.

Methodology in Plain English

Each ISO is modeled as a graph whose vertices are the settlement points traders actually transact against — 4 zones for CAISO, 8 for ERCOT, 8 for MISO, 15 for NYISO, and 21 for PJM. For each zone, prices are normalized over the trailing context so the encoder sees shape rather than level, then cut into non-overlapping patches and mapped to tokens by a projection shared across all zones and markets.

A temporal transformer processes each zone independently, after which a cross-zone attention step lets zones exchange information. That attention is augmented with two additive biases: a fixed adjacency matrix built from market-map proximity, and a price-correlation matrix recomputed at each forecast origin. Two learned scalars weight these biases, so the model can use topology or ignore it. A probabilistic decoder predicts nine quantile levels plus an optional locational correction, split into a market-wide term and a zone-centered term summed to zero, scaled by a single learned gate initialized at zero — meaning the decomposition begins switched off and its learned magnitude reports what it is actually worth.

Training proceeds in two stages. First, the model is trained on pooled source-ISO data to get a shared initialization. Then it is refined with chronological meta-learning episodes — an earlier support set and a later query set — using first-order MAML, so the objective rewards fast adaptation to a new distribution rather than in-distribution accuracy. At evaluation, a held-out ISO is given its map-derived graph, and if a causal adaptation set exists, the same support-style update is applied. The number of adaptation steps is selected per ISO on validation MAE, never on the test year. Splits are identical everywhere: training through 2023-12-31, validation over 2024, testing over 2025.

Architecture specifics include a 16-hour patch length over a 336-hour (14-day) context, model width 384, six attention heads, four transformer layers, feed-forward width 1536, dropout 0.1, and 2000 outer meta-training steps with five inner steps at η = 10⁻³.

Why This Matters

The paper reframes an old constraint as an opportunity: instead of asking how to squeeze more out of one market's few years of history, it asks what is transferable across markets and what must stay market-specific. Because price formation across ISOs is driven by shared physics and largely common market design, cross-market history functions as a pretraining corpus rather than out-of-distribution noise. The result is a model whose parameter count is independent of the number of pricing zones, tested under leave-one-ISO-out conditions where the target market differs in zone count, topology, and generation mix.

Real-world applications:

• Day-ahead bidding and trading: participants must submit bids before the auction closes, so a next-day LMP forecast is what bidding decisions are made against.
• Risk management and hedging: the model predicts quantiles, not just point values, supporting probabilistic exposure estimates.
• Storage, hydro, and flexible-asset scheduling: charge/discharge or release decisions depend on expected price spreads across zones and hours.
• Utility and retail procurement: zone-level price forecasts inform contract positions and load-serving obligations.

Industry relevance: the benchmark includes the largest and most heterogeneous markets in the U.S. — PJM with 21 transmission-owner zones across thirteen states, NYISO with eleven internal load zones plus four proxy interfaces, ERCOT with eight tightly coupled load zones, MISO with eight regional hubs, and CAISO with four default load aggregation points. A ~90x parameter reduction relative to a large time-series foundation model, combined with better average accuracy, is directly relevant to operators who need low-latency, low-cost inference. The paper also states that all price and load-forecast data are public ISO market-portal downloads and that code is available in a public GitHub repository.

Future Directions

1. Extend from zonal settlement points to nodal LMPs, increasing the graph size and structural complexity beyond the 4–21 zone graphs studied here.

2. Add more exogenous features to the inputs, which currently consist only of trailing prices, day-ahead load forecasts, and calendar features.

3. Address the documented failure modes: MetaGrid is outperformed on ERCOT by time-series foundation models, adaptation degrades MISO, and price spikes are underpredicted — suggesting work on scarcity regimes and on when adaptation helps versus hurts.

4. Trace system-level effects: the authors report forecast accuracy only and explicitly leave propagation into dispatch and hedging decisions as future work.

Target Audience

Researchers and practitioners in machine learning for power systems, electricity market analysts, and forecasters at ISOs, utilities, and trading firms who already understand day-ahead market mechanics. It will also interest meta-learning and time-series foundation model researchers looking for a domain where cross-task transfer, variable graph size, and strict chronological leakage control all matter simultaneously. Beginners would need substantial background in transformers, meta-learning, and locational marginal pricing before the methodology is accessible.

Authors’ abstract

Day-ahead (DA) electricity price forecasting is usually posed per market, with a separate model fitted to each grid's own history. This caps accuracy: statistical and tree-based baselines saturate, while higher-capacity sequence models need more training data than a single market's few years of hourly prices can supply. Such methods also treat each node as an independent series, discarding the spatial dependencies induced by network topology and congestion. Because price formation across independent system operators (ISOs) is driven by shared physics and largely common market design, we instead treat cross-market history as a pretraining corpus. We present MetaGrid, a topology-aware transformer, meta-trained across markets so that a single zone-count-independent parameter set adapts to an unseen grid. On a leak-free benchmark of five U.S. ISOs, where every model receives the same prices, DA load forecasts and calendar features, MetaGrid attains the lowest average MAE, improving on the best baseline by 3.1\% and on the same architecture trained from scratch by 7.7\%.