Energy MLP in Energy Systems

Updated 17 October 2025

Energy MLPs are feedforward neural networks with multiple fully connected layers and nonlinear activations used to model complex energy system behaviors.
They are applied in forecasting, price prediction, digital twin modeling, and predictive control, achieving high accuracy and efficiency.
Their design integrates advanced feature engineering, temporal encoding, and system constraints to enable real-time scheduling and robust grid management.

An Energy MLP, in the context of energy systems and power engineering, refers to the application of multi-layer perceptrons (MLPs)—that is, feedforward neural networks—as function approximators, predictors, or control agents for modeling, forecasting, optimization, and decision-making in energy-related domains. Energy MLPs are employed for diverse tasks spanning short-term forecasting, optimal scheduling, price prediction, data-driven digital twins of operational constraints, and direct control of distributed resources. Their mathematical structure typically comprises fully connected layers equipped with nonlinear activation functions (such as ReLU or sigmoid), enabling the capture of intricate nonlinear dependencies among multiple input features such as load, weather, operational state, economic signals, and spatiotemporal system variables.

1. Neural Network Fundamentals in Energy MLPs

Energy MLPs are instantiated as feedforward neural networks, commonly formulated as:

ŷ = f_L(W_L * f_{L-1}(…f_1(W_1x + b_1)… ) + b_L)

with layers indexed by ℓ, weight matrices W_ℓ, bias vectors b_ℓ, and nonlinear activation functions f_ℓ, typically ReLU, sigmoid, or tanh. Input features routinely encode physical parameters (e.g., power flows, energy consumption, time indices, weather conditions), engineered representations (such as cyclic time encodings: sin(2πt/T), cos(2πt/T)), and categorical variables (via one-hot encoding of device, site, or market id).

Energy MLP architectures vary in depth and width, from shallow two-layer models used for basic consumption estimation (Snoeck et al., 21 Aug 2024), up to deep networks exceeding hundreds of units per layer for high-dimensional scenario classification and dispatch reconstruction (Pagnier et al., 2022). Sequential and time-series modeling is addressed either via explicit inclusion of lagged variables in the input (auto-regressive MLPs (Wu et al., 7 Oct 2024)), or by extension with recurrent architectures (e.g., GRU or LSTM), although the MLP formulation remains central to many approaches.

2. Methodological Spectrum: Forecasting, Control, and Surrogate Modeling

Energy MLPs exhibit remarkable versatility:

Short-term forecasting: Extreme Learning Machines (ELMs)—single-hidden-layer feedforward networks with randomly initialized weights—are employed for multi-variate, multi-output short-term production forecasting (solar, wind, thermal, hydro, imports) across large hourly datasets. The closed-form solution for ELM output weights via the pseudo-inverse minimizes computational burden, supporting real-time applications (Voyant et al., 18 Aug 2025). Models achieve nRMSE of ~0.18 for solar and ~0.05 for thermal, with R² often exceeding 0.98 on 1-hour horizons.
Price prediction: The evolution of electricity price forecasting is marked by transition from linear regression models to small single-hidden-layer neural networks (early energy MLPs), and eventually to deep MLPs and hybrid architectures—including probabilistic DNNs producing predictive distributions (Jędrzejewski et al., 2022). These structures enable accurate, tractable forecasting across day-ahead and real-time market timeframes.
Digital twin surrogates: MLPs as digital twins for optimal power flow market clearing tasks: deep, multi-layer perceptrons are trained to classify the set of binding transmission constraints (lines at thermal limits) and reconstruct the associated dispatch and locational marginal prices using grid-aware linear recovery (Pagnier et al., 2022). A four-layer MLP with 500 units per layer is employed for grid scenario classification, facilitating rapid solution of dispatch equations and LMP calculations.
Scheduling and predictive control: Hybrid time-series MLPs, informed by physics-based modeling, are mapped onto multi-scale integrated energy systems. Day-ahead scheduling exploits a long-term ReLU-based MLP surrogate recast exactly as a mixed-integer linear program (MILP), while fast and slow MLP surrogates facilitate distributed economic MPC at minute and second resolutions, yielding >70% improvement in overall system performance versus benchmarks (Wu et al., 7 Oct 2024).
Reinforcement Learning Agents: Within MARL frameworks for community-wide and prosumer-centric energy management (e.g., V2G, asset optimization), policy (actor) and value (critic) networks are implemented as MLPs, learning mappings from local and global observations to continuous-valued energy actions. Performance improvements (e.g., >10–35% reductions in various grid KPIs) are realized using multi-agent Deep Deterministic Policy Gradient with energy MLP structures (Fonseca et al., 2 Apr 2024).

3. Feature Engineering and Temporal Encodings

The feature engineering paradigm in energy MLPs leverages time-windowed data (sliding windows on historical features (Voyant et al., 18 Aug 2025)), cyclic encodings (sin/cos transforms for daily/weekly periodicities), spatial featurization (segment, route, zone properties), and contextual augmentation (weather, regulatory text, asset metadata).

Tables summarizing model features:

Model	Input Features	Output
MIMO ELM (Voyant et al., 18 Aug 2025)	Sliding window, cyclic encoding	Multi-energy forecasts
RET (Snoeck et al., 21 Aug 2024)	Segment+route features, temp, speed	EV route energy consumption
DNN for EPF (Jędrzejewski et al., 2022)	Lagged prices, loads, market attributes	24h price series

Advanced models further utilize function call modules for post-processing and chain-of-thought reasoning in LLMs (EF-LLM), as well as multimodal inputs fusing numeric and textual descriptions (Qiu et al., 30 Oct 2024).

4. Integration with System Constraints, Physical Models, and Optimization

Energy MLPs are often combined with explicit formulations of physical and operational system constraints:

In optimal scheduling and market clearing, neural network surrogates are assembled or recast into MILP forms by expressing ReLU or other activations via mixed-integer representations (Wu et al., 7 Oct 2024).
Surrogate models are structured hierarchically: operating unit MLPs are “stitched together” via energy balance or process equations, yielding composite system predictors across time scales.
Market clearing twins respect duality and KKT conditions by only reconstructing dispatch/state and LMPs for binding constraints, preserving economic and feasibility guarantees in most high-frequency scenarios (Pagnier et al., 2022).
In logistics-grid equilibrium coupling, MLPs and RL-derived policies (PU-MDP for e-truck fleets) interact with dual variables from grid OPF, yielding dynamic feedback loops challenging traditional static analysis (Yao et al., 7 May 2025).

5. Performance, Trade-offs, and Evaluation

Energy MLPs deliver substantial accuracy and efficiency improvements in the cited applications:

Energy forecasting using ELM shows lower nRMSE versus persistence and competitive accuracy relative to LSTM, while delivering 25x lower training time (due to closed-form output layer solution). MIMO ELM architectures yield marginal gain over SISO but improve error balancing (Voyant et al., 18 Aug 2025).
RET models (decoder-only transformers sized via Chinchilla scaling laws) reach up to +217 basis points lower MAPE than feed forward NN for last-mile EV energy estimation, particularly outperforming baselines on challenging/extreme condition routes (Snoeck et al., 21 Aug 2024).
In market clearing, digital twin MLPs drastically increase computation efficiency, maintaining dispatch and price reconstruction with near-linear scaling; model accuracy is sensitive to constraint classification, with robust duality in most cases (Pagnier et al., 2022).
Hybrid energy MLPs enable scheduler/controller performance gains, e.g., >70% total system improvement, >25% vs. day-ahead baselines, and better responsiveness to operator and customer objectives (Wu et al., 7 Oct 2024).
MARL energy management with MLP actors/critics secures reductions of >11–35% on grid operational KPIs while enabling individualization across prosumers (Fonseca et al., 2 Apr 2024).
Novel architectures (EF-LLM) achieve lower MAE/RMSE than traditional models, especially in sparse/extreme event scenarios, and provide statistical consistency/reliability via hallucination detection and multi-task loss controls (Qiu et al., 30 Oct 2024).

6. Applications, Adaptability, and Future Directions

Energy MLPs are deployed for:

Grid and market forecasting (EPF, price, load, renewables)
Route-level energy estimation for EV logistics and delivery (Snoeck et al., 21 Aug 2024)
Real-time asset scheduling, predictive control in IES, HVAC, and distributed storage/demand response (Wu et al., 7 Oct 2024)
Edge-based prosumer-centric control (V2G, demand response, community energy optimization) (Fonseca et al., 2 Apr 2024)
Market digital twins for competitive scenario evaluation (Pagnier et al., 2022)
Modular energy KPI reporting and semantic interoperability via machine-readable descriptors (Reiche et al., 26 Sep 2024)

Their adaptability is supported by feature engineering, context-aware input structures, and the ability to handle diverse data sources and operational constraints. Future research involves improving physical-model integration, reducing computational complexity in online tasks, hybridizing MLP surrogates with deeper architectures, and enhancing robustness against volatility, system heterogeneity, and regulatory requirements.

7. Comparison with Other Approaches and Limitations

Energy MLPs are compared with persistence, AR, LASSO, SISO, LSTM, and transformer architectures:

Offer competitive or superior accuracy with much lower computational cost (particularly for ELM or standard feedforward MLPs).
Computational efficiency favors real-time and online operation.
Interpretability is often higher for ELM/MLP than deeper recurrent or transformer models.
Limitations include degradation of accuracy with increased prediction horizons (noted for volatile renewables (Voyant et al., 18 Aug 2025)), sensitivity to input feature selection, and challenges in mapping high-dimensional topological or system constraints directly (suggesting future work in GNNs (Pagnier et al., 2022)).
Scalability is feasible via model and data engineering, but real-time deployment for very large system models may require surrogate reduction or hybridization.

In aggregate, Energy MLPs represent a mature, rigorously evaluated subclass of neural networks that enable high-accuracy, efficient, and adaptable prediction, optimization, and control for a spectrum of energy system problems, with extensive empirical validation and broad prospects for future methodological extension.