EAC-mp: Diverse Domain Approaches

• EAC-mp is an overloaded abbreviation used to denote context-specific methods across epistemic message passing, air combat algorithms, charge-density prediction, and quantum chemistry corrections.
• Its implementations range from a compositional framework for dynamic epistemic updates and a reinforcement learning approach in multi-agent combat to a symmetry-preserving deep learning model for electronic structure.
• The term’s ambiguity necessitates careful interpretation of underlying formalisms and notations, as each domain carries unique methodologies and limitations.

Searching arXiv for the exact term and the cited IDs to verify the usages and metadata. EAC-mp is an overloaded abbreviation used in multiple, technically unrelated research contexts. In the supplied literature, it denotes at least four distinct constructs: a compositional framework for epistemic message passing realized through the e-calculus, a shorthand referring to the air-combat algorithm ACE-MAPPO, the Materials Project–trained variant of EAC-Net for charge-density prediction, and the MP-like denominator variant within EA/IP-CC($P$;$Q$) theory. This suggests that EAC-mp is not a field-stable term but a context-dependent abbreviation whose meaning must be determined from domain and notation (Xing, 2022).

1. Nomenclature and scope

The broadest and most explicit use of EAC-mp in the supplied material is Epistemic Action/Calculus for Message Passing, realized in the e-calculus as a framework that merges process-calculus style message passing with dynamic epistemic logic, specifically action model logic, in order to model how agents’ knowledge evolves through synchronous and asynchronous communication (Xing, 2022). In a different domain, the abbreviation is stated to match ACE-MAPPO, the “Adversarial Curriculum and Evolutionary-enhanced Multi-agent Proximal Policy Optimization” method for cooperative beyond-visual-range air combat (Li et al., 24 May 2026). In materials informatics, EAC-mp denotes the large-scale Materials Project–trained variant of EAC-Net for charge-density prediction (Xuejian et al., 6 Aug 2025). In quantum chemistry, the same string is used for the MP-like denominator choice, the A variant, in the CC($P$;$Q$) extension to EA/IP-EOMCC (Gururangan et al., 19 Jun 2025).

A common misconception is that EAC-mp names a single method. The supplied sources directly contradict that interpretation. The term therefore functions less as a canonical acronym than as a local shorthand embedded in specific subfields.

2. Epistemic Action/Calculus for Message Passing

In the e-calculus paper, EAC-mp is a compositional framework that extends the $\pi$-calculus with operators for sending and receiving basic facts and ties these events to epistemic updates through action models (Xing, 2022). The problem addressed is the mismatch between dynamic epistemic logics, which capture epistemic state change, and asynchronous distributed systems, where communication has interactive, structural, and environmental aspects. As stated there, asynchronous announcement logic focuses on logical laws for change of epistemic state after receiving information, but does not model the interactive behaviors between an agent and its environment.

The control layer is process-theoretic. Standard $\pi$-calculus prefixes such as $\overline{a}c$, $a(z)$, and $\tau$ are enriched with fact prefixes $\overline{a}q$ and $Q$0. Processes are embedded in e-systems of the form

$Q$1

where processes are associated with agents. The epistemic layer is semantic: agents’ knowledge is represented by Kripke models

$Q$2

and communications are represented by action models

$Q$3

The interaction between the two layers is mediated by product update: $Q$4

The operational semantics integrates process transitions with epistemic updates. Non-fact actions alter only the control term. Fact input by an agent triggers an epistemic product update, and fact output is constrained by a truthfulness precondition requiring that the sender knows the fact. In the synchronous fact-communication rule, a rendezvous between sender and receiver induces a joint product update by an action model $Q$5, so that knowledge transfer is represented within the transition system itself. This coupling of structural operational semantics and action-model update is the central feature of the framework.

Asynchrony is captured operationally by buffer pools implemented as processes. Two constructions are given. In the FIFO buffer pool, chained cells are linked by aliases, so readers traverse a controlled sequence such as $Q$6, and name passing prevents readers from jumping ahead. In the arbitrary-order buffer pool, each cell exposes visiting channels to agents, so cells can be read in any order but only once. In both constructions, name passing, restriction, and scope extrusion supply the mechanism by which the buffer topology is created and navigated. The paper’s comparison with asynchronous announcement logic is precise: AAL hard-wires private FIFO channels from a trusted public source, whereas EAC-mp models explicit message-passing infrastructure between agents and supports FIFO or arbitrary read order through process constructions rather than through the logic alone.

The framework also states several formal properties. These include bisimulation invariance under action model execution, knowledge preservation for facts already known, receiver knowledge gain after reception, preservation of receiver knowledge under truthful passing, idempotence of repeating the same interaction, and commutativity of executable epistemic interactions. The stated applications include robotic coordination, multi-UAV cooperation, satellite detection, and protocol design in which message order and accessibility matter. The stated limitations are equally important: verification complexity and decidability are not analyzed, time and probabilistic delays are not modeled, and richer phenomena such as suspicion or deception would require extended action-model schemas.

3. ACE-MAPPO in cooperative air combat

In the air-combat paper, the query term EAC-mp is explicitly identified with ACE-MAPPO, a hybrid MARL framework for beyond-visual-range $Q$7 cooperative UCAV combat that combines MAPPO with evolutionary mechanisms and adversarial curriculum learning (Li et al., 24 May 2026). The problem is formulated as a Dec-POMDP under centralized training and decentralized execution. Blue agents act independently on local observations, while training uses a centralized value function on global state for credit assignment.

The environment is a rectangular theater of $Q$8 by $Q$9 with initial altitude $P$0 and initial speed $P$1. Each aircraft carries four air-to-air missiles. Episodes terminate at $P$2 minutes or when one team is completely eliminated; the team with more surviving aircraft at the time limit wins, and ties are possible. Each Blue agent receives a $P$3-dimensional local observation partitioned into self state, relative situation, and threat perception. The action space is discrete with $P$4 tactical commands, including turning, climb, dive, acceleration, deceleration, notch maneuver, S-shaped lateral oscillation, and missile launch.

ACE-MAPPO keeps the MAPPO actor–critic backbone with parameter sharing for homogeneous Blue agents and a centralized critic $P$5. The policy objective is the clipped PPO loss

$P$6

with generalized advantage estimation and a value loss under CTDE. The reward is the composite form

$P$7

with $P$8, $P$9, and $Q$0. Terminal outcome gives $Q$1 for win and $Q$2 for loss. The dense geometric term rewards favorable nose-on geometry and proximity, while the threat term penalizes unsafe states under missile threat.

The method augments MAPPO through three coupled modules. First, a population-based genetic soft update periodically creates a population of mutated policies around the current actor by entropy-regularized mutation, evaluates them for fitness, and softly injects elite parameters when the elite fitness exceeds the current actor’s by a threshold $Q$3. The population size is $Q$4, evaluations use $Q$5 rounds, and evolution runs every $Q$6 episodes. Second, evolutionary-augmented prioritized trajectory replay stores both RL trajectories and elite evolutionary trajectories in a hybrid buffer and prioritizes replay using a metric that mixes advantage magnitude, normalized return, and a source boost for elite evolutionary data. Third, adversarial evolutionary curriculum learning maintains an opponent pool whose policies are scored by win rate against a rule-based policy and sampled from a truncated Gaussian centered at a curriculum mean $Q$7 that increases as the Blue policy improves.

The reported experimental results are specific. The average win rate in a rolling window of $Q$8 episodes rises quickly and stabilizes around the $Q$9th episode at approximately $\pi$0, with decreased variance. Relative to MAPPO, RMAPPO, IPPO, and EMARL, ACE-MAPPO is reported to converge fastest and achieve the highest steady performance. In $\pi$1 randomized matches against each baseline, it attains a significant win-rate advantage against RMAPPO, MAPPO, EMARL, and dominates IPPO. The ablation results assign distinct roles to the three modules: without genetic update, early learning is slower; without prioritized trajectory replay, win-rate growth is shallower; without curriculum, high win rate against a fixed opponent does not translate into robust generalization. The paper’s practical interpretation is that evolution broadens search and helps escape local optima, prioritized trajectory replay improves reuse of sparse high-value episodes, and adversarial curriculum reduces overfitting to narrow opponent distributions.

4. EAC-mp as the Materials Project variant of EAC-Net

In the charge-density paper, EAC-mp is the large-scale Materials Project–trained variant of EAC-Net, a symmetry-preserving deep learning framework for predicting real-space charge density as a sum of learned atom-centered contributions (Xuejian et al., 6 Aug 2025). The central decomposition is

$\pi$2

where each partial density is anisotropic and environment-dependent. A schematic local-frame parametrization is

$\pi$3

with angular structure represented through spherical harmonics and coefficients learned from local chemical environments.

EAC-Net enforces symmetry through SE(3)-equivariant features implemented with e3nn. Features are organized in irreducible representations of SO(3), and equivariant message passing uses Clebsch–Gordan tensor products. The key architectural innovation highlighted in the paper is the atom–grid coupling block, which transfers equivariant atomic descriptors directly to spatial grid points through spherical-harmonics-based kernels. Unlike purely grid-based models that aggregate local atomic descriptors into grid features, EAC-Net keeps per-atom-to-grid edges and decodes atomic contributions directly. Scalar edge features are compressed and passed to a two-head decoder,

$\pi$4

where the value head proposes atom-wise contributions and the weight head distributes importance among neighboring atoms. The EAC-mp variant uses the MLP+S weight design.

The reported EAC-mp training set consists of 48,183 configurations from Materials Project, collected in August 2025, each with 5,000 sampled grid points from CHGCAR. Sampling combines random, density-weighted, gradient-weighted, and core-focused strategies. The evaluation metric is the normalized mean absolute error

$\pi$5

The stated hyperparameters for EAC-mp are $\pi$6, feature dimension $\pi$7, four atom-interaction convolution layers, two edge-update layers, approximately $\pi$8 million parameters, atom and grid cutoffs of $\pi$9 and $\pi$0, and training for $\pi$1 steps with Adam, exponential learning-rate decay from $\pi$2 to $\pi$3, and batch size between $\pi$4 and $\pi$5 on two NVIDIA RTX A6000 GPUs.

The paper states that EAC-mp achieves state-of-the-art accuracy comparable to existing large charge-density models while retaining atom-wise decomposability and efficiency. On more than $\pi$6 frames outside the training distribution, it achieves $\pi$7 for the vast majority of elements, with typical values around $\pi$8 across the periodic table. Reported examples include amorphous Si with $\pi$9, Al–Mg alloy with $\overline{a}c$0, and spin-polarized Fe with total-density $\overline{a}c$1 and spin-density $\overline{a}c$2. The model also supports downstream non-self-consistent workflows: the predicted density can be used to construct the effective Kohn–Sham potential through Poisson’s equation and then used for NSCF band-structure, force, or energy calculations. Reported NSCF errors include $\overline{a}c$3 in energy and $\overline{a}c$4 in forces for a perturbed $\overline{a}c$5-atom Si supercell.

5. EAC-mp in EA/IP-CC($\overline{a}c$6;$\overline{a}c$7) theory

In quantum chemistry, EAC-mp refers to the MP-like denominator choice, the A variant, in the CC($\overline{a}c$8;$\overline{a}c$9) extension to electron-attachment and ionization-potential EOM coupled-cluster methods (Gururangan et al., 19 Jun 2025). The underlying framework begins from the CCSD ground state

$a(z)$0

and the similarity-transformed Hamiltonian

$a(z)$1

EA and IP target states are represented as

$a(z)$2

with EOM eigenvalue equation

$a(z)$3

The CC($a(z)$4;$a(z)$5) idea is to solve the EOM problem in an active model space $a(z)$6 and then add a noniterative correction from the complementary space $a(z)$7: $a(z)$8 The correction is expressed through moments

$a(z)$9

and coefficients

$\tau$0

The denominator can be chosen in two forms. The D variant uses EN-like denominators based on diagonal matrix elements of $\tau$1. The A variant, identified in the supplied material as the EAC-mp choice, replaces them with Møller–Plesset-style denominators based on orbital energies or an MP partition of $\tau$2.

The specific realizations are EA/IP-CC(t;3) methods, in which the $\tau$3 space contains all lower-rank sectors together with an active subset of triples-like configurations: $\tau$4–$\tau$5 determinants for EA and $\tau$6–$\tau$7 determinants for IP. The dominant triples are thus iterated, while the remainder enters through the noniterative CC($\tau$8;$\tau$9) moment correction. The paper states that these approaches achieve sub-millihartree accuracies relative to full EA-EOMCCSD($\overline{a}q$0–$\overline{a}q$1)/IP-EOMCCSD($\overline{a}q$2–$\overline{a}q$3) data with reduced computational effort, and improve upon EA/IP-CR-EOMCC(2,3).

The numerical benchmarks are detailed. For CH, CNC, and C$\overline{a}q$4N in the EA sector, EA-CC(t;3)A errors are reported in the range of approximately $\overline{a}q$5–$\overline{a}q$6, while EA-CC(t;3)D reaches values near $\overline{a}q$7 to $\overline{a}q$8. For SH, N$\overline{a}q$9, and NCO in the IP sector, IP-CC(t;3)A errors are reported up to $Q$00, with IP-CC(t;3)D up to $Q$01. The stated interpretation is that D-denominator variants are generally more robust, while the A, MP-like variant remains accurate and useful. The paper recommends EA/IP-CC(t;3)D by default, with EA/IP-CC(t;3)A, the EAC-mp choice, as an alternative when appropriate.

6. Cross-domain ambiguity, interpretation, and limitations

Across the supplied sources, EAC-mp spans epistemic process theory, multi-agent reinforcement learning, equivariant machine learning for electronic structure, and equation-of-motion coupled-cluster theory (Xing, 2022). The same character string therefore denotes, respectively, a message-passing epistemic calculus, a hybrid MAPPO-based air-combat learner, a Materials Project–trained charge-density model, and an MP-like denominator variant inside CC($Q$02;$Q$03). This suggests that abbreviation matching alone is insufficient for identification; the surrounding formalism is decisive.

The ambiguity has practical consequences. In epistemic logic, EAC-mp is tied to $Q$04-calculus syntax, Kripke semantics, and product updates. In air combat, it is recognizable by CTDE, PPO objectives, curriculum opponent pools, and evolutionary replay. In charge-density modeling, it is identifiable through SE(3)-equivariant atom–grid coupling, CHGCAR supervision, and normalized density errors. In quantum chemistry, it appears with EA/IP-EOMCC notation, $Q$05–$Q$06 or $Q$07–$Q$08 sectors, and CC($Q$09;$Q$10) moment corrections. A plausible implication is that any technical reading of EAC-mp should begin by locating the associated mathematical objects: channels and action models, policy/value functions, equivariant kernels and charge fields, or similarity-transformed Hamiltonians and denominator choices.

The sources also delineate domain-specific limitations. The e-calculus formulation does not analyze verification complexity and does not model temporal or probabilistic delays. ACE-MAPPO adds compute overhead through population evaluation, opponent-pool maintenance, and replay-buffer management. EAC-mp for charge density has reduced accuracy for structurally disordered systems, spin densities, and sparsely represented heavy elements. The MP-like EAC-mp choice in CC($Q$11;$Q$12) may overcorrect or undercorrect when the diagonal of $Q$13 is strongly renormalized. These limitations are not shared across meanings; they are local to each usage, which further reinforces that EAC-mp is not a unified method but a recurrent abbreviation applied to unrelated technical programs.