SEFOS: Ocean Modeling & SystemC Verification

Updated 10 July 2026

SEFOS is an acronym with dual definitions in computational ocean modeling and hardware verification, denoting distinct technical entities.
In FESOM2, SEFOS implements a split‐explicit external solver that enhances phase accuracy and runtime performance while preserving the mean ocean state.
In SystemC verification, SEFOS modifies the symbolic execution engine to verify peripherals without altering the original kernel, ensuring cross‐level consistency.

SEFOS is an ambiguous acronym used in at least two unrelated arXiv research contexts. In computational ocean modeling, it denotes the split-explicit external-mode solver introduced for the Finite volumE Sea ice-Ocean Model, FESOM2, as an alternative to the model’s existing semi-implicit barotropic solver (Banerjee et al., 2023). In hardware verification, it denotes Symbolic Execution For Original SystemC, a cross-level symbolic-execution framework that preserves the original SystemC kernel and peripheral under verification while adapting the symbolic-execution engine instead (Rudkowski et al., 5 Sep 2025). The two usages share neither methodology nor application domain; precise interpretation therefore depends entirely on disciplinary context.

1. Nomenclature and scope

The acronym is not used uniformly across the literature. One usage is rooted in geophysical fluid dynamics and numerical time integration for ocean circulation models, while the other is rooted in symbolic execution for SystemC peripherals. The resulting polysemy is substantive rather than stylistic: each SEFOS names a specific technical artifact with its own algorithmic assumptions, evaluation regime, and comparison baselines (Banerjee et al., 2023, Rudkowski et al., 5 Sep 2025).

Domain	SEFOS usage	Core object
Ocean modeling	Split-explicit external-mode solver for FESOM2	Barotropic/external-mode time-stepping option
Hardware verification	Symbolic Execution For Original SystemC	Engine-modified symbolic execution of SystemC peripherals

This ambiguity also creates predictable retrieval problems. The acronym should not be conflated with SEFI, a segmentation-free integration method for retinal spatial transcriptomics (Chelebian et al., 8 Feb 2025), with SEFDM-oriented communication work (Shamsi et al., 2023), or with the SEP forecasting system SOFIE (Liu et al., 12 Nov 2025). A plausible implication is that disambiguation by full title or arXiv identifier is often necessary in bibliographic searches.

2. SEFOS in FESOM2: numerical role and update structure

In FESOM2, SEFOS is the new split-explicit external or barotropic mode solver, introduced as an alternative to the semi-implicit solver already used in the model (Banerjee et al., 2023). Its defining strategy is to separate the fast external mode from the slower baroclinic three-dimensional dynamics. The baroclinic equations are advanced with a relatively large time step $\tau$ , while the barotropic equations are subcycled using $M$ smaller substeps of size $\tau/M$ . The implementation uses an asynchronous formulation in which scalar quantities such as elevation, temperature, salinity, and layer thickness are defined at full time steps $n$ , whereas velocities and transports are defined at half steps $n+1/2$ .

The specific scheme adopted is the dissipative asynchronous forward-backward time-stepping method of Demange et al. (2019). A dissipation parameter $\theta$ damps spurious fast oscillations and removes the need for a separate filter; the paper notes $\theta = 0.14$ as a recommended setting. Because the method is intrinsically dissipative, it avoids the expensive two-step filtering otherwise needed to center the solution in time. The barotropic update is coupled to the three-dimensional dynamics through vertically integrated forcing, and the transport predictor includes advection, Coriolis, pressure-gradient, horizontal viscosity, and implicit vertical viscosity terms.

The paper formulates the layer momentum equation in flux form and then applies a predictor-corrector structure for the transport. After the barotropic solve, the three-dimensional transports are “trimmed” so that their vertical sum matches the barotropic transport. This design is central to how SEFOS preserves compatibility with ALE coordinates and with the broader FESOM2 dynamical core.

3. ALE coordinates, phase accuracy, and computational performance

A major part of the FESOM2 SEFOS formulation concerns Arbitrary Lagrangian-Eulerian vertical coordinates, especially $Z^*$ and $\tilde{Z}$ (Banerjee et al., 2023). For the simple $Z^*$ coordinate, the new thickness is scaled with free-surface height according to

$M$ 0

with $M$ 1. For more general ALE coordinates such as $M$ 2, thickness prediction depends on horizontal divergence within layers, making the intermediate-time thickness harder to determine. The paper explicitly identifies this as a reason for formulating momentum in terms of transports $M$ 3 rather than directly in terms of velocities and thicknesses.

In the appendix, the $M$ 4 implementation is approximated by splitting divergence into a quasi-barotropic part and a residual part,

$M$ 5

with a high-frequency thickness correction evolved by

$M$ 6

This suggests that the simplest ALE case is operationally straightforward, whereas the more general ALE formulation requires explicit management of divergence-driven thickness changes and additional smoothing or relaxation to keep layer thickness positive and smooth.

The accuracy and efficiency results are favorable relative to the semi-implicit solver. In linear wave analysis, SEFOS has much smaller phase error than the SI solver, especially at high Courant numbers. Both SE and SESM can achieve low dissipation, but SE is simpler and far more phase-accurate than the semi-implicit method; SESM can be slightly more accurate than SE, but SE is simpler and scales better. In idealized and realistic ocean-sea ice simulations, the mean ocean state remains very similar to the SI solver, with only small differences in sea surface height, surface temperature, and diffusivity. One reported physical difference is a modest increase in eddy kinetic energy outside the equatorial belt, attributed to reduced overall dissipation. Performance gains are clearest at high parallelization levels, roughly below 400 vertices per core, where SEFOS shows better runtime performance and parallel scalability across all tested workloads.

4. SEFOS as Symbolic Execution For Original SystemC

In hardware verification, SEFOS stands for Symbolic Execution For Original SystemC and names the “original-SystemC” branch of a cross-level verification framework for peripherals (Rudkowski et al., 5 Sep 2025). Its core design decision is to leave both the SystemC kernel and the peripheral design under verification unmodified, and instead modify the symbolic-execution engine. The paper positions SEFOS as the opposite design point to CrosSym, which modifies and replaces the SystemC kernel.

This distinction is motivated by the structure of standard SystemC implementations. The original kernel uses system threads for SC_THREADs, mutex-based synchronization in the signal and port mechanism, and large C++ objects that create costly solver queries. Rather than translating these features away by replacing the kernel, SEFOS adapts KLEE 3.1 to understand SystemC scheduling semantics directly. The paper emphasizes that SystemC concurrency is cooperative multitasking rather than true parallel execution: processes run sequentially and yield at synchronization points such as wait(). SEFOS exploits that property by intercepting the pt_* thread-handling calls used by the PThread-based SystemC implementation and representing each SystemC thread as its own symbolic-execution context with a stack and program counter.

The framework supports three verification scenarios: standalone TLM peripheral verification, standalone RTL peripheral verification, and cross-level RTL $M$ 7TLM verification. The cross-level mode is the key novelty. A higher-level implementation and a lower-level implementation of the same peripheral can be symbolically executed together so that refinement steps are checked against an abstract reference model. This is especially relevant where an RTL implementation coexists with a TLM model and the lower-level test bench can be derived from the already specified higher-level behavior.

5. Engine-level mechanisms and empirical evaluation

A SEFOS-specific optimization is array minimisation, introduced to reduce SMT-solver cost for large SystemC objects (Rudkowski et al., 5 Sep 2025). The paper represents an object by a state array $M$ 8 and an update list $M$ 9. For an access $\tau/M$ 0, SEFOS computes an approximation using only relevant entries, written as $\tau/M$ 1. For the state array, it retains entries satisfying

$\tau/M$ 2

For symbolic updates, it includes any update $\tau/M$ 3 such that $\tau/M$ 4 might be true. The paper describes this as an intentional over-approximation that may preserve some impossible entries while avoiding loss of any potentially relevant one. Because it requires engine modification, it is presented as specific to the SEFOS design point.

The evaluation covers four peripherals—PLIC, GCD, Hash, and Map—each available in both RTL and TLM, allowing standalone and cross-level scenarios. The experiments use STP as the SMT solver, a 24-hour timeout, a 4 GB memory limit, a 120-second per-solver-query limit, and BFS as the search strategy. For SEFOS, array minimisation is enabled in the main experiments. The functional-verification study identifies real implementation bugs, including an inverted priority/threshold bug in the PLIC RTL model and a signed/unsigned conversion bug in GCD. Neither SEFOS nor CrosSym automatically found one known infinite-loop bug, because the corresponding path was explored but not completed before timeout.

The paper also reports a 300+ mutant evaluation, in which controlled mutations are inserted into the four peripherals and the functional test cases are run with a 15-minute maximum runtime, stopping at the first detected error. SEFOS is reported as often slightly better or comparable depending on the scenario, with bug-finding success depending not only on the number of explored paths but on whether BFS reaches the right ones within the time budget. When compared directly with CrosSym, SEFOS usually requires more memory and sometimes more time because of the original SystemC startup and the complexity of the unmodified kernel. CrosSym is therefore usually a bit faster and uses less memory. However, SEFOS retains the original SystemC environment, and in some tests its runtime is close to CrosSym’s; in one cross-level test, SEFOS finishes while CrosSym times out. Array minimisation is especially important: in the PLIC case study, it cuts some runs from timeouts to completions in roughly 1 hour and 9 hours, and in one test reduces runtime by about 95%, albeit with noticeably higher memory use.

6. Comparative significance and persistent sources of confusion

The two SEFOS usages are methodologically unrelated, but each is defined by a fidelity-preserving intervention in a difficult computational setting. In FESOM2, the intervention is a split-explicit external-mode integrator that preserves a mean ocean state very similar to the semi-implicit baseline while improving phase accuracy and scalability (Banerjee et al., 2023). In SystemC verification, the intervention is an engine-modified symbolic-execution stack that preserves the original SystemC kernel and peripheral while enabling standalone and cross-level verification scenarios (Rudkowski et al., 5 Sep 2025). This suggests a family resemblance at the level of engineering intent—retain a trusted host environment while moving complexity into a more specialized subsystem—even though the domains and mechanisms are entirely distinct.

A common misconception is to treat SEFOS as a single standardized acronym across arXiv. The evidence does not support that interpretation. Nearby acronyms designate unrelated systems: SEFI concerns segmentation-free integration of nuclei morphology and spatial transcriptomics (Chelebian et al., 8 Feb 2025); SEFDM work addresses spectrally efficient frequency-division multiplexing under Doppler and delay spread (Shamsi et al., 2023); SOFIE is a solar energetic particle forecasting system in the Space Weather Modeling Framework (Liu et al., 12 Nov 2025). For technical citation, indexing, and literature review, the term is therefore best handled as a domain-specific identifier whose meaning must be fixed by the surrounding paper title, abstract, and application area.