American Multi-Modal Energy System (AMES)

• AMES is a unified framework that integrates U.S. bulk-level electric, natural gas, oil, and coal infrastructures using invariant SysML and hetero‐functional graph theory.
• It employs a GIS-driven clustering algorithm to convert heterogeneous asset data into a normalized architectural model for structural and comparative analysis.
• The system facilitates resilience assessment and decarbonization policy evaluations by revealing cross-modal interdependencies and regional energy characteristics.

The American Multi-Modal Energy System (AMES) is the United States’ integrated system-of-systems comprising four critical energy infrastructures: the electric grid, the natural gas system, the oil system, and the coal system. It is “multi-modal” because it simultaneously represents multiple energy carriers, or operands, together with their conversion, transport, storage, and consumption processes across heterogeneous physical assets and facilities. In the AMES literature, the system is formalized at two complementary levels: as an invariant SysML reference architecture for consistent model specification, and as a hetero-functional graph for structural analysis that preserves both form and function across modalities (Thompson et al., 2020, Thompson et al., 2022).

1. Definition, system boundary, and architectural invariants

AMES is defined as a system-of-systems rather than a single network because each constituent infrastructure is a value chain in its own right, yet each exchanges energy and mass with the others and depends on the others for processing, transport, and conversion. The reference architecture models the United States bulk, or wholesale and transmission-level, infrastructures and their connections across a clearly defined system boundary. End-use sectors and distribution-level or retail assets lie outside that modeled boundary. The top-level SysML internal block diagram includes the four AMES subsystems together with external entities such as domestic supply sources, energy imports and exports, the natural environment, domestic consumption, and water treatment (Thompson et al., 2020).

A central distinction in the AMES framework is between the reference architecture and instantiated architectures. The reference architecture is invariant through the sustainable energy transition: it preserves the system boundary, subsystem definitions, classes of assets, allocated activities, and interface and flow types. Instantiated architectures are case-specific realizations mapped onto that reference form; what changes are asset ratios, technology mix, capacities, schedules, operational policies, and scenario parameters such as demand and fuel prices. This distinction is important because AMES is intended to support comparative modeling across regions and scenarios without redefining the underlying architecture each time (Thompson et al., 2020).

The modeled operands include both matter and energy carriers. Across the two AMES papers, these include coal, raw natural gas, processed natural gas, crude oil, processed oil, syngas, liquid biomass, solid biomass, solar irradiance, wind energy, uranium, water energy, electric power, withdrawn water, mine effluent, processing effluent, and thermal effluent. This suggests that AMES is not restricted to commodity transport alone; it also encodes conversion chains, resource dependencies, and environmental interfaces in a unified architectural description.

2. Constituent infrastructures and cross-modal couplings

The electric grid portion of AMES includes substations, transmission lines, generators by fuel or technology, and consumption nodes. The natural gas system includes raw and processed gas production, processing plants, compressor stations, pipelines, and import or export terminals. The oil system includes crude and processed oil production, refineries, pipelines, terminals and ports, and import or export facilities. The coal system includes mines, coal transport links such as rail, conveyor, and barge, and coal-fired generators (Thompson et al., 2022).

The defining feature of AMES is not merely coexistence of these infrastructures but their interdependence. Gas-fired power plants convert processed natural gas into electricity. Compressor stations move raw and processed gas and often consume electricity. Refineries process crude oil into refined products and consume electricity. Coal supply chains transport coal to generators and industrial consumers. In hetero-functional terms, “Generate Electric Power from Processed Gas” depends on “Transport Processed Gas” and “Process Raw Gas”; “Compress processed gas” is electrically driven; “Process Crude Oil” is adjacent to electricity consumption capabilities; and “Transport Coal” connects extraction or storage buffers to “Generate Electric Power from Coal” (Thompson et al., 2022).

A recurrent misconception is to treat AMES as an electricity model with attached fuel inputs. The formalism described in the AMES literature is broader. It includes multiple operands, multiple process classes, multiple resource classes, and explicit cross-system interfaces. Conversely, it is not a full end-use or retail model: the electric grid ends at substations, and retail oil and gas delivery such as small gas lines, tankers, gas stations, and homes are omitted. The scope is therefore integrated but intentionally bulk-level rather than exhaustive (Thompson et al., 2020).

3. GIS-driven model construction and model-based systems engineering

The structural AMES model is built from Platts Map Data Pro GIS layers covering electric, natural gas, oil, and coal assets, including asset attributes and GPS coordinates. The workflow removes cancelled, closed, or illegible assets, then creates physical continuity between point-type resources and line-type resources by means of a novel operand-guided geographic clustering algorithm. The algorithm proceeds in three stages: primary clustering at 0.1 miles, clustering points and line endpoints by compatible operand; secondary clustering at 1 mile, adding remaining isolated nodes into like-operand clusters; and tertiary clustering at 35 miles, connecting remaining isolated nodes to nearby clusters by introducing new transportation resources of the same operand. Isolated point resources are then removed, and the cleaned GIS data are mapped to AMES reference architecture entities and converted to XML for the open HFGT toolbox (Thompson et al., 2022).

This preprocessing pipeline is methodologically consequential because the original GIS layers are heterogeneous and transmission-focused. The clustering algorithm preserves operand compatibility, but it also introduces model-based inference by creating new transportation resources and connections within specified distance thresholds. The resulting structural model is therefore open and reproducible, yet not a literal transcription of source data. A plausible implication is that AMES balances empirical geospatial grounding with architectural normalization needed for graph-theoretic analysis.

The principal network primitives are buffers, transportation resources, capabilities, and operands. Buffers are point facilities such as substations, generators, refineries, processing plants, terminals, ports, and mines. Transportation resources are line-type assets such as transmission lines, pipelines, and rail or barge links. Capabilities are allocated functions expressed as subject-plus-verb-plus-object sentences, such as generation, processing, compression, import or export, transport, and consumption. Operands are the tracked energy or mass carriers, such as electricity, raw gas, processed gas, syngas, crude oil, processed oil, coal, water energy, and biomass (Thompson et al., 2022).

The reported computational profile indicates that scaling is dominated by GIS processing and XML generation rather than by hetero-functional graph computation. For the USA model, XML generation is reported at approximately 51,470.68 seconds and the HFGT run at approximately 6,439.74 seconds; XML size is 420.7 MB and HFG pickle size is 682.6 MB. The paper characterizes the observed scaling as roughly linear with system size, described as “$2N$” behavior (Thompson et al., 2022).

4. Hetero-functional graph formulation

Hetero-functional graph theory encodes the allocation of function onto form in a multi-modal, heterogeneous system. In the AMES formulation, a system operand is “An asset or object $l_i \in L$ that is operated on or consumed during the execution of a process.” A system process is “An activity $p \in P$ that transforms a predefined set of input operands into a predefined set of outputs.” A system resource is “An asset or object $r_v \in R$ that is utilized during the execution of a process.” A resource is a buffer $b_s \in B_S$ if it is capable of storing one or more operands at a unique location in space, and a capability is an action $e_{wv} \in {\cal E}_S$ defined by a system process $p_w$ being executed by a resource $r_v$ (Thompson et al., 2022).

The core structural objects are the positive and negative hetero-functional incidence tensors, the formal graph adjacency matrix, and the hetero-functional adjacency matrix. The negative tensor $\widetilde{\cal M}_\rho^-$ records when a capability pulls operand $l_i$ from buffer $l_i \in L$0; the positive tensor $l_i \in L$1 records when a capability injects operand $l_i \in L$2 into buffer $l_i \in L$3. Summing over operands yields buffer-capability incidence matrices

$l_i \in L$4

from which the formal graph adjacency is computed as

$l_i \in L$5

After matricizing the incidence tensors to $l_i \in L$6, the hetero-functional adjacency is

$l_i \in L$7

The formal graph therefore captures physical connectivity between buffers, whereas the hetero-functional graph captures feasible sequences of capabilities linked by a shared operand-buffer pair (Thompson et al., 2022).

The operational meaning of this construction is explicit. If capability $l_i \in L$8 injects operand $l_i \in L$9 into buffer $p \in P$0 and capability $p \in P$1 pulls the same operand from the same buffer, then

$p \in P$2

and

$p \in P$3

This is the exact mechanism by which the model represents gas-fired generation, electrically driven gas compression, refinery electricity consumption, and coal-to-electric linkages. It also clarifies why the formal graph loses modality-specific heterogeneity when operands are summed out, whereas the hetero-functional graph retains full cross-modal detail (Thompson et al., 2022).

5. Reported structural characteristics and regional differentiation

The paper reports structural models for New York, California, Texas, and the United States. In the formal graph, the number of operands is 13 for New York and California, and 14 for Texas and the United States. The number of buffers is 7,686 in New York, 16,754 in California, 197,108 in Texas, and 473,321 in the United States. The number of edges is 9,115, 20,674, 179,895, and 511,802 respectively. Formal-graph adjacency sparsity is $p \in P$4 for New York, $p \in P$5 for California, $p \in P$6 for Texas, and $p \in P$7 for the United States. In the hetero-functional model, the number of capabilities is 43,766 in New York, 100,349 in California, 1,430,588 in Texas, and 3,130,235 in the United States; HFG adjacency sparsity is $p \in P$8, $p \in P$9, $r_v \in R$0, and $r_v \in R$1 respectively (Thompson et al., 2022).

These statistics support several regional interpretations reported by the paper. Texas has by far the largest number of buffers and edges among the states, and its adjacency matrices are much sparser; the United States aggregate is the sparsest overall. Texas also has the highest buffers-per-land density, buffers-per-population density, edges-per-land density, edges-per-population density, capability-per-land density, and capability-per-population density among the listed states. The paper interprets this as reflecting Texas’s large energy infrastructure, especially oil and gas, and notes that Texas strongly influences USA-wide statistics (Thompson et al., 2022).

The normalized buffer-type distributions further differentiate regional structure. Substations comprise 74.6% of buffers in New York, 76.8% in California, 69.3% in Texas, and 66.0% in the United States. Electric generation facilities comprise 13.5%, 16.8%, 4.6%, and 6.4% respectively, with the remainder consisting of oil and gas terminals, refineries, processing plants, mines, and other facility types that vary by region. Texas has relatively more oil and gas facilities, while the United States contains more coal facilities than Texas (Thompson et al., 2022).

Capability distributions and fuel mixes are likewise region-specific. Electric power capabilities dominate across regions, especially California. Texas and the United States have similar capability distributions, but the United States exhibits much more coal-related capability than Texas. New York, Texas, and the United States show pronounced natural-gas import and export capabilities, whereas California shows a larger share of electric generation capabilities, including solar, hydro, and natural-gas ramping. Natural gas is the leading electric generation capacity in all regions; New York has relatively more processed oil and nuclear capacity than California and Texas; California has substantial solar and hydro capacity; Texas has substantial wind; and California and New York have largely transitioned away from coal while Texas and the United States retain significant coal capacity (Thompson et al., 2022).

The reported degree distributions are non-classic but systematic. Formal-graph degree distributions share a peak at degree 1, a dip at degree 2, a secondary rise near degree 3, and then an exponential tail. Hetero-functional in-degree and out-degree distributions show long exponential tails with similar shapes, peaks at degrees 2 and 4, and dips near degree 3. The paper also reports process-wise three-dimensional in-degree and out-degree distributions showing power-law behavior within each process class. This suggests that AMES contains structurally prominent process classes that may accumulate additional interconnections over time, with implications for infrastructure lock-in and transition dynamics (Thompson et al., 2022).

6. AMES-3D, behavioral estimation, and limitations

The structural work on AMES is embedded in the NSF AMES-3D project, “American Multi-Modal Energy System Synthetic Simulated Data.” Its purpose is to develop open-source structural and behavioral machine-learning models and synthetic or simulated data for interdependent critical infrastructures. Within that program, the structural models provide the topology, capability allocation, and operand-flow constraints, while behavioral models are intended to learn and simulate flows, dynamics, dispatch, ramping, import and export behavior, demand swings, and resilience behavior subject to physics and controls. The XML inputs and hetero-functional graph outputs produced by the structural analysis constitute the structural backbone for those later behavioral models (Thompson et al., 2022).

A later behavioral extension is the Weighted Least Squares Error Hetero-functional Graph State Estimation model, which applies HFGT to estimate optimal flows of mass and energy through AMES with asset-level granularity. In its AMES-specific form, the estimator uses a steady-state conservation constraint

$r_v \in R$2

together with aggregated measurement equations

$r_v \in R$3

and capacity constraints such as $r_v \in R$4. The paper reports applications to a Western Region and an Eastern Region, using EIA demand, generation, and withdrawal data together with Platts capacity data, and identifies regional seasonal patterns and residual mismatches that reflect structural constraints and conflicting measurements (Thompson et al., 23 Sep 2025).

Several limitations are explicit in the AMES literature. The source data are transmission-focused, so the electric model ends at substations and excludes distribution networks and rooftop solar. Retail oil and gas delivery are omitted. The clustering algorithm introduces inferred connections within 0.1-mile, 1-mile, and 35-mile thresholds. The formal graph abstraction loses operand detail because it sums over operands before computing adjacency. The current structural scope emphasizes incumbent modes—electricity, gas, oil, and coal—while future work is expected to incorporate hydrogen, synthetic fuels, bio-energy, and additional interdependencies (Thompson et al., 2022).

The planning significance of AMES follows from these structural and behavioral capabilities. The hetero-functional graph preserves cross-modal pathways and can identify vulnerabilities such as compressor stations that depend on electric supply and fuel-to-power couplings that propagate outages. Density measures indicate infrastructure intensity per land area and per capita. Process-wise power-law behavior suggests that new low-carbon processes may require policy support to overcome incumbent network advantages. The papers also argue that electrification has structural benefits because electric power distribution penetrates closer to end-use periphery than fossil-fuel supply chains do. Taken together, AMES provides an integrated framework for resilience assessment, sustainability analysis, decarbonization policy, and transparent scenario testing across the major U.S. energy carriers (Thompson et al., 2022, Thompson et al., 23 Sep 2025).