Mycelium: A Generalizable Cross-Grid Multi-Task Model for Electrical Distribution Systems

Zhengyang Wei; Shourya Bose; Helgi Hilmarsson; Elena Carnio; Dhruv Suri

cs.LGSep 27, 2026

Mycelium: A Generalizable Cross-Grid Multi-Task Model for Electrical Distribution Systems

Authors: Zhengyang Wei, Shourya Bose, Helgi Hilmarsson, Elena Carnio, Dhruv Suri

Organizations: Stanford University · Pravāh

Abstract

Electrical distribution grid operations require inference across heterogeneous networks from sparse, noisy, and incomplete time series measurements. In this work, we identify challenges and explore solutions towards a unified model that can perform diverse tasks grounded in the physics of the electric grid and generalize to unseen distribution networks. We define a unified grid ontology that represents variable sized distribution networks as heterogeneous graphs while preserving native topology, asset types, and electrical relationships across networks. We develop a physics based data simulation pipeline that combines reference and procedurally generated distribution networks with network reconfigurations, fault scenarios, and configurable sensing conditions. We present Mycelium, a heterogeneous graph transformer with structure aware communication edges and electrical reference features that encode network position and nominal phase orientation, together with task specific temporal readouts which generate per task outputs. We train Mycelium on reference as well as synthetic grids, and study its generalization on benchmark networks completely excluded from training and validation. Mycelium is observed to outperform task specific neural baselines on most reported benchmark metrics. Architectural ablations and the aforementioned studies reveal Mycelium's capability to learn representations of the underlying physics which serves to enhance cross-task performance, thereby addressing a significant challenge in unified grid models.

Figures & tables

Figure 1: Mycelium architecture. (a) A heterogeneous graph models network components and electrical relations. (b) Type specific encoders embed attributes and temporal measurements. (c) A shared heterogeneous graph transformer performs spatial message passing. (d) Task specific temporal heads support SE, PA, SW, and fault diagnosis.

Figure 2: Mycelium’s message passing graph inherits the base grid topology and adds communication edges. Blue dashed edges connect the substation to transformer primary buses, and red dashed edges connect customers to their serving transformer’s secondary bus.

Split	Networks
Train	SMART-DS AUS/SFO ( $70\%$ each); registered IEEE feeder; EPRI ckt5 , ckt24 ; D-Suite spd_r/s/u
Validation	SMART-DS AUS/SFO ( $15\%$ each); EPRI ckt7 ; D-Suite spm_s
Test	SMART-DS AUS/SFO ( $15\%$ each) and all GSO; D-Suite spm_r/u
Benchmark	Iowa 240- and 296-bus; European industrial, rural, and urban

Table 1: Network level assignments.

			State estimation				Phase	Switch			Fault
Split	Baseline	Task	p.u. $\downarrow$	$v_{\mathrm{mag}}$ (V) $\downarrow$	$v_{\mathrm{ang}}$ (deg) $\downarrow$	$v_{\mathrm{mag}}$ MAPE (%) $\downarrow$	acc $\uparrow$	prec $\uparrow$	rec $\uparrow$	F1 $\uparrow$	det F1 $\uparrow$	class 5 $\uparrow$	loc $\uparrow$	hop@1 $\uparrow$	hop@2 $\uparrow$	hop@3 $\uparrow$
Test	CANOS ( Piloto et al., 2024 )	State est.	0.00221	2.86	0.576	0.136	-	-	-	-	-	-	-	-	-	-
	GraphSAGE-CPI ( Dande et al., 2025 )	Phase	-	-	-	-	0.3276	-	-	-	-	-	-	-	-	-
	DGS-GNN ( Ebtia et al., 2024 )	Switch	-	-	-	-	-	0.0807	0.2399	0.1207	-	-	-	-	-	-
	STGATv2 ( Karabulut et al., 2026 )	Fault	-	-	-	-	-	-	-	-	-	-	0.1349	0.2162	0.2683	0.3107
	Mycelium 10k	All four	0.00345	5.99	1.107	0.234	0.5713	0.9960	0.8137	0.8957	1.0000	0.4840	0.1710	0.2369	0.2999	0.3314

Table 2: Mycelium and task-specific neural baselines on the held-out test split and frozen benchmark. Dashes indicate tasks a baseline does not model. Lower is better for state estimation errors and higher is better otherwise. Best values within each split are bold.

		State estimation				Phase	Switch			Fault
Split	Configuration	p.u. $\downarrow$	$v_{\mathrm{mag}}$ (V) $\downarrow$	$v_{\mathrm{ang}}$ (deg) $\downarrow$	MAPE (%) $\downarrow$	Acc. $\uparrow$	Prec. $\uparrow$	Rec. $\uparrow$	F1 $\uparrow$	Det. F1 $\uparrow$	class 5 $\uparrow$	Loc. $\uparrow$	Hop@1 $\uparrow$	Hop@2 $\uparrow$	Hop@3 $\uparrow$
(a) Test	No communication	0.00370	4.99	1.286	0.240	0.6611	0.1950	0.9800	0.3253	1.0000	0.4540	0.1819	0.2743	0.3464	0.3822
	Random communication	0.00316	5.24	1.083	0.230	0.6328	0.9631	0.9056	0.9334	1.0000	0.4241	0.1881	0.2628	0.3267	0.3583
	Mycelium 10k	0.00345	5.99	1.107	0.234	0.5713	0.9960	0.8137	0.8957	1.0000	0.4840	0.1710	0.2369	0.2999	0.3314
Benchmark	No communication	0.01866	77.46	1.639	5.955	0.4256	0.7945	0.9968	0.8842	1.0000	0.7143	0.1878	0.2950	0.3492	0.4034
	Random communication	0.01805	78.24	1.543	5.773	0.4231	0.8721	0.9910	0.9278	0.9993	0.6468	0.1971	0.2857	0.3135	0.3810

Table 3: Architectural ablations on the test split and benchmark: (a) communication edges and (b) nominal angle references. Random rewiring preserves edge counts and endpoint types per relation and network. Training data and optimization remain fixed. Best values are bold.

		State estimation				Phase	Switch			Fault
Split	Configuration	p.u. $\downarrow$	$v_{\mathrm{mag}}$ (V) $\downarrow$	$v_{\mathrm{ang}}$ (deg) $\downarrow$	MAPE (%) $\downarrow$	Acc. $\uparrow$	Prec. $\uparrow$	Rec. $\uparrow$	F1 $\uparrow$	Det. F1 $\uparrow$	class 5 $\uparrow$	Loc. $\uparrow$	Hop@1 $\uparrow$	Hop@2 $\uparrow$	Hop@3 $\uparrow$
(a) Test	Reference only	0.00881	7.63	0.933	0.320	0.5846	0.9992	0.9178	0.9568	1.0000	0.3455	0.1526	0.2305	0.2899	0.3249
	+25% synthetic	0.00302	4.45	1.116	0.197	0.5922	0.9806	0.9542	0.9672	1.0000	0.4708	0.1839	0.2820	0.3437	0.3721
	Mycelium 10k	0.00345	5.99	1.107	0.234	0.5713	0.9960	0.8137	0.8957	1.0000	0.4840	0.1710	0.2369	0.2999	0.3314
Benchmark	Reference only	0.04025	148.88	2.388	7.714	0.3539	0.9445	0.9946	0.9689	1.0000	0.2937	0.1323	0.1799	0.2249	0.3016
	+25% synthetic	0.01991	141.51	1.134	5.669	0.3886	0.9585	0.9958	0.9768	1.0000	0.6111	0.1429	0.2156	0.2500	0.3056

Table 4: Data scaling on the test split and benchmark: (a) synthetic corpus fractions added to the full reference set with a 10,000-bus cap, and (b) training network size caps with full synthetic augmentation. Mycelium 10k is the shared reference, and evaluation sets remain fixed. Best values are bold.

	Run	State estimation				Phase	Switch			Fault
Split		p.u. $\downarrow$	$v_{\mathrm{mag}}$ (V) $\downarrow$	$v_{\mathrm{ang}}$ (deg) $\downarrow$	$v_{\mathrm{mag}}$ MAPE (%) $\downarrow$	acc $\uparrow$	prec $\uparrow$	rec $\uparrow$	F1 $\uparrow$	det F1 $\uparrow$	class 5 $\uparrow$	exact $\uparrow$	hop@1 $\uparrow$	hop@2 $\uparrow$	hop@3 $\uparrow$
Test	SE only	0.00148	3.33	1.057	0.148	-	-	-	-	-	-	-	-	-	-
	Phase only	-	-	-	-	0.5363	-	-	-	-	-	-	-	-	-
	Switch only	-	-	-	-	-	0.8325	0.9374	0.8818	-	-	-	-	-	-
	Fault only	-	-	-	-	-	-	-	-	0.7990	0.5322	0.1927	0.2731	0.3441	0.3768
	Mycelium 10k	0.00345	5.99	1.107	0.234	0.5713	0.9960	0.8137	0.8957	1.0000	0.4840	0.1710	0.2369	0.2999	0.3314

Table 5: Joint versus single-task training with the same backbone on the test split and frozen benchmark. Dashes mark untrained tasks. Lower is better for state estimation errors and higher otherwise. Best values per split are bold.

Figure 3: Single-task finetuning on the test split and frozen benchmark, shown in the top and bottom rows. Hatching denotes combined reference and synthetic finetuning data. Lower is better for state estimation errors and higher is better otherwise.

Appendix figures & tables13 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 4: Structural characteristics of the reference corpus and the five frozen benchmark networks: bus count (a), independent loop count (b), electrical extent in hops from the substation (c), and customer density (d). Histograms show corpus distributions, colored vertical lines mark benchmark networks, and dashed lines indicate corpus medians. The table reports benchmark percentile ranks. Bus count and customer density use logarithmic horizontal axes.

Trigger	Change to the proposed model	Repetition limit
Low snapshot voltage	Rebalance single-phase loads where connections permit; adjust transformer taps; add capacitors or regulators; add parallel conductors along affected paths; select a larger transformer.	Ordered passes; up to 4 conductor reinforcement and 2 transformer upgrade rounds.
High snapshot voltage	Enable inverter volt-var control, back off voltage boosting taps where the low voltage condition permits, reinforce conductors, or reduce affected DER output limits by 20%.	Up to 5 rounds.
Snapshot overload, with thermal enforcement	Add parallel conductor circuits, choose a larger transformer, add parallel substation units, or increase regulator capacity.	Up to 3 rounds.
Daily voltage violation	Adjust taps or reinforce affected paths for undervoltage; use inverter control, tap backoff, phase rebalancing, or DER curtailment for overvoltage.	Up to 2 undervoltage and 8 overvoltage rounds.

Appendix

Table 6: Repair actions used during synthetic network generation. Actions apply to the affected service areas or branches, subject to the sampled design’s equipment options. Snapshot repairs also seek voltage headroom beyond the final acceptance limits.

Task	ML formulation	Prediction scope
State estimation (SE)	Continuous regression	Magnitude and angle per (bus, phase, timestep)
Phase attribution	Three-class classification	One A/B/C assignment per eligible consumer and window
Switch state inference	Binary classification	One open/closed state per switch and window
Fault diagnosis	Six-class classification; conditional localization	Normal/fault class per window; equipment location for faulted windows

Appendix

Table 7: Prediction problems and temporal scope.

Type	Static inputs / connectivity	Temporal inputs
(a) Nodes
Bus	Base voltage; source bus indicator; normalized coordinates and coordinate validity flag.	Per phase voltage magnitude and angle; active power $P$ and reactive power $Q$ .
Consumer	One-hot metering tier encoding.	Customer voltage channels for phase attribution and voltage derived from the metering tier; active and reactive power.
Substation	Positive- and zero-sequence source resistance and reactance; three-phase and single-phase short-circuit strengths; base voltage; voltage setpoint; source angle; frequency.	Feeder head voltage and active/reactive power when feeder head fusion is enabled.
Capacitor	Voltage and reactive power ratings; switching step count; delta connection and controller indicators; active step fraction.	–
DER	Device kind encoding for PV, generator, or storage; active/reactive power ratings; delta connection indicator.	–

Appendix

Table 8: Model inputs for nodes (a), relations (b), and auxiliary stores (c). Every temporal measurement has an observability mask. Connectivity only relations provide endpoint indices and relation identity without separate attribute vectors. DT denotes distribution transformer. Dashes indicate no direct temporal input. Auxiliary entries describe their inputs and role across the last two columns.

Figure 5: Nominal angle parameterization on an example network. Columns show phases A, B, and C. (a) Nominal references $\theta^{\mathrm{nom}}$ encode source and transformer phase conventions. (b) Residuals $\Delta\theta=\operatorname{wrap}(\theta-\theta^{\mathrm{nom}})$ capture operating angle deviations. Nominal values use categorical colors, and residuals share a continuous scale. Light gray markers indicate absent phases, and solid and dashed edges denote lines and transformers, respectively. Angles are shown in degrees.

Component	Setting
Transformer layers	8
Hidden dimension	128
Attention heads	4
Node type FFN hidden width	256
Temporal window	24 hourly steps
Positional encoding	$9\rightarrow 16$ dimensions

Appendix

Table 9: Mycelium configuration. Parameter count includes the task heads.

Tier	Bus voltage	DT meter (joint $V{+}I$ )	Branch flow	Customer $P$ / $Q$	of which $Q$
sparse	1%	60%	0.5%	10%	20%
medium	5%	90%	2%	30%	20%
dense	15%	100%	5%	70%	20%
clean	100%	100%	100%	100%	100%

Appendix

Table 10: Structural coverage per tier. A “DT meter” is one physical device: its terminal bus voltage and transformer edge current channels are always granted together, never sampled independently. Customer coverage is a binary AMI/unobserved split. Among AMI customers, reactive power is reported by the stated fraction. The substation reference voltage and feeder head

P

Q

are observed under every policy.

Network	Policy	WLS		Ours
		Result	Time	Result	Time
240_bus	nm_dense	34.0 (.0091) / .63	7s	10.3 (.0022) / .67	.4s
	nm_medium	11.4 (.0029) / .23	7s	13.8 (.0026) / .81	.4s
	nm_sparse	18.8 (.0049) / .35	6s	13.0 (.0028) / .80	.4s
	ami_dense	21.6 (.0057) / .40	7s	12.4 (.0024) / .76	.4s
	ami_medium	34.0 (.0091) / .63	8s	9.9 (.0022) / .65	.4s

Appendix

Table 11: State estimation errors and per-case runtimes for WLS and Mycelium across benchmark networks and sensor policies. Each result is voltage magnitude MAE in volts (per unit) / voltage angle MAE in degrees.

\dagger

marks WLS divergence, and

\ddagger

marks urban cases in which WLS did not converge and returned its initialization.

	CANOS				Ours
Policy	MAE (V)	MAE (p.u.)	MAE ( ∘ )	MAPE	MAE (V)	MAE (p.u.)	MAE ( ∘ )	MAPE
clean	1.98	.0017	.63	0.35%	18.71	.0079	1.77	5.43%
nm_dense	6.21	.0100	3.83	4.97%	116.36	.0145	1.37	5.31%
nm_medium	10.24	.0205	4.15	6.28%	135.07	.0166	1.32	5.38%
nm_sparse	12.96	.0276	3.66	7.31%	140.04	.0186	1.36	5.58%
ami_dense	8.74	.0113	3.53	5.73%	22.08	.0063	1.99	5.25%

Appendix

Table 12: Per policy state estimation on the benchmark (all five networks, with fault, 24 timesteps).

Method	Benchmark	Test
correlation-based ( $P_{\mathrm{xfmr}}$ )	0.3999	0.5741
correlation-based ( $P{+}Q_{\mathrm{xfmr}}$ )	0.4200	0.3637
Mycelium 10k	0.4001	0.5713
Mycelium 20k	0.4387	0.6150

Appendix

Table 13: Pooled phase attribution accuracy. Populations are matched to the models’:

n{=}1{,}315{,}577

on the benchmark,

n{=}2{,}862

on the test split.

Policy	Model	Det. F1	class 5	Loc.	Hop@1	Hop@2	Hop@3
clean	STGATv2	-	-	0.213	0.250	0.269	0.306
clean	Mycelium	1.000	0.704	0.500	0.537	0.583	0.583
nm_dense	STGATv2	-	-	0.130	0.213	0.222	0.306
nm_dense	Mycelium	1.000	0.704	0.185	0.315	0.370	0.435
nm_medium	STGATv2	-	-	0.130	0.231	0.241	0.296
nm_medium	Mycelium	1.000	0.769	0.185	0.324	0.361	0.417

Appendix

Table 14: Fault diagnosis by sensor policy on the frozen benchmark, with 108 faulted samples per policy for localization. Det. F1 is the fault versus normal detection F1 obtained by collapsing the fault class matrix. Class 5 is the 5-way type accuracy among genuinely faulted samples. Higher is better for all metrics. Best comparable values within each policy are bold, including ties.

Network	Model	$n$	Det. F1	class 5	Loc.	Hop@1	Hop@2	Hop@3
240_bus	STGATv2	189	-	-	0.159	0.159	0.159	0.159
240_bus	Mycelium	189	1.000	0.667	0.312	0.455	0.481	0.545
296_bus	STGATv2	189	-	-	0.005	0.090	0.138	0.201
296_bus	Mycelium	189	1.000	0.788	0.116	0.270	0.307	0.307
industrial	STGATv2	126	-	-	0.127	0.127	0.127	0.254
industrial	Mycelium	126	1.000	0.754	0.214	0.238	0.310	0.381

Appendix

Table 15: Fault diagnosis by network on the frozen benchmark, pooled across sensor policies.

n

counts faulted samples used for localization. Det. F1 is the fault versus normal detection F1 obtained by collapsing the fault class matrix. Class 5 is the 5-way type accuracy among genuinely faulted samples. Higher is better for all metrics. Best comparable values within each network are bold.

		State estimation				Phase	Switch			Fault
Split	Configuration	p.u. $\downarrow$	$v_{\mathrm{mag}}$ (V) $\downarrow$	$v_{\mathrm{ang}}$ (deg) $\downarrow$	MAPE (%) $\downarrow$	Acc. $\uparrow$	Prec. $\uparrow$	Rec. $\uparrow$	F1 $\uparrow$	Det. F1 $\uparrow$	class 5 $\uparrow$	Loc. $\uparrow$	Hop@1 $\uparrow$	Hop@2 $\uparrow$	Hop@3 $\uparrow$
Benchmark	240_bus ( $n{=}259$ )	0.0039	18.26	0.870	0.63	–	–	–	–	1.000	0.6667	0.3122	0.4550	0.4815	0.5450
	296_bus ( $n{=}259$ )	0.0034	18.32	0.742	0.76	–	–	–	–	1.000	0.7884	0.1164	0.2698	0.3069	0.3069
	industrial ( $n{=}196$ )	0.0097	40.66	1.213	60.92	–	0.9974	0.5955	0.7458	1.000	0.7540	0.2143	0.2381	0.3095	0.3810
	rural ( $n{=}259$ )	0.0059	2.70	1.286	0.59	0.4898	0.9644	0.9564	0.9604	1.000	0.7831	0.1852	0.3175	0.3333	0.4444
	urban ( $n{=}70$ )	0.0342	318.20	2.971	1.40	0.3782	0.9777	0.9714	0.9746	1.000	0.4286	0.0794	0.2063	0.2857	0.2857

Appendix

Table 16: Per-network performance of Mycelium 10k on the frozen benchmark. Network macro averages weight networks equally within each metric’s evaluation population. Pooled metrics aggregate predictions across networks. Sample counts

n

refer to evaluation windows. Phase attribution has eligible targets only on the rural and urban networks. Superscripts

k

indicate the number of networks included when fewer than five contribute. All results use the same checkpoint and evaluation run.

Power Systems

Power systems research studies the planning, operation, control, and protection of electrical grids and their integration with energy resources.

See all 231 papers

Physics-Aware Distillation of a Grid Foundation Model for Real-Time Edge Inference
Oct 15, 2026Vlad Alexandru Sănduleac, Shahariya Rasheed Rayamarakkarveettil Puthanpurayil, Noman Khan +1Knowledge Distillation Power Systems
Faculty of Power Engineering, National University of Science and Technology POLITEHNICA Bucharest, Bucharest, Romania · AAU Energy, Aalborg University, Aalborg, Denmark
TokaMind for Power Grid: Cross-Domain Transfer from Fusion Plasma
May 10, 2026JC Wu, Norton Lee, Kai Siang ChenTime Series Classification Critical Slowing Down
TaiScience Research Group, affiliated with Fu Jen Catholic University, Taiwan · Center for Geometry and Physics, Institute for Basic Science (IBS), South Korea · Fu Jen Catholic University, Taiwan
Cross-Market Meta-Learning for Electricity Price Forecasting
Oct 12, 2026Delaram Pirhayatifard, Terrence AlsupElectricity Price Forecasting Time Series Forecasting
Rice University, Houston, TX · Morgan Stanley, New York, NY

Oct 15, 2026J/K move · Enter open · S save

Physics-Aware Distillation of a Grid Foundation Model for Real-Time Edge Inference

Vlad Alexandru Sănduleac, Shahariya Rasheed Rayamarakkarveettil Puthanpurayil, Noman Khan, Remus Teodorescu

Faculty of Power Engineering, National University of Science and Technology POLITEHNICA Bucharest, Bucharest, Romania · AAU Energy, Aalborg University, Aalborg, Denmark

Knowledge Distillation Power Systems Efficient Neural Network Inference Optimal Power Flow

Open paper AskPDF arXiv

Grid foundation models (GridFMs) are graph transformers pretrained on a masked power-flow objective, and evaluate power flow orders of magnitude faster than an iterative solver. Their size, however, targets data-centre inference, whereas low-inertia operation increasingly asks for inference at the edge, next to the measurement, at batch size one and within a single synchrophasor (PMU) reporting frame. We distil a 20.1M-parameter, 12-layer GridFM teacher into a 0.62M-parameter, 6-layer student, a

32.5\times

parameter reduction at half the message-passing depth, using an objective that combines the masked power-flow loss with output, physics-residual, latent-state and attention transfer. The physics-residual term, which matches the teacher's power-residual profile, has not previously been applied to typed power-grid graphs. We evaluate on a renewable variant of the IEEE 118-bus benchmark grid in which 26 of the conventional (synchronous) generators are replaced by inverter-based renewables with battery flexibility and standardised reactive-power limits (IEEE 1547), giving

97\,529

physically valid (AC-OPF-feasible) operating scenarios, and we ablate all eight combinations of the transfer terms, reporting accuracy against ground truth and fidelity to the teacher separately. Distillation lowers student error on all four predicted quantities, by up to

48\%

on active-power dispatch, and every distilled student is more accurate than its teacher on reactive-power dispatch. The gain is largely carried by the output matching term. The physics-residual term, in the layer-aggregated form used here, is consistently harmful, which we attribute to the spatial averaging it applies to a bus-level residual field. The resulting student is

32.5\times

smaller in parameter count and has half the message-passing depth, making it a candidate for subsequent edge-device benchmarking.

Abstract

Power Systems

Explore similar work

Physics-Aware Distillation of a Grid Foundation Model for Real-Time Edge Inference

TokaMind for Power Grid: Cross-Domain Transfer from Fusion Plasma

Cross-Market Meta-Learning for Electricity Price Forecasting