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arxiv: 2606.07681 · v1 · pith:CGV5SESMnew · submitted 2026-06-04 · 💻 cs.SE · cs.AI· cs.CE· cs.MA

Systematic LLM Translation of Legacy Scientific Code to Differentiable Frameworks: Application to a Land Surface Model

Aya Lahlou , Linnia Hawkins , Pierre Gentine This is my paper

Pith reviewed 2026-06-27 23:55 UTC · model grok-4.3

classification 💻 cs.SE cs.AIcs.CEcs.MA
keywords LLM translationFortran to JAXdifferentiable programmingland surface modelagentic pipelinenumerical equivalenceJacobian computationscientific code migration
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The pith

An LLM agent pipeline translates a 19,000-line Fortran land surface model into equivalent differentiable JAX code.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a five-phase LLM-based pipeline to convert legacy Fortran scientific code into JAX. Static dependency analysis orders translation from the call graph, iterative compile-repair loops fix errors, and a Fortran reference oracle enforces numerical parity at the module level before integration. Applied to CLM-ml-v2, the resulting model computes the complete Jacobian in one backward pass, recovers parameters in eight times fewer steps than gradient-free optimization, and runs 24 times faster than sequential Fortran at ensemble size 2,048. This enables gradient-based methods on existing large models without manual recoding.

Core claim

The pipeline converts the full CLM-ml-v2 Fortran land surface model to JAX while maintaining numerical equivalence. The translated model computes the complete Jacobian in a single backward pass, recovers physical parameters in eight times fewer steps than gradient-free optimization, and achieves a 24 times wall-clock speedup over sequential Fortran at ensemble size N=2,048. The model and pipeline infrastructure are released as a reusable framework.

What carries the argument

The five-phase LLM-based agentic pipeline that orders modules via static dependency analysis on the call graph, applies iterative compile-repair loops, and uses a Fortran reference oracle to enforce module-level numerical parity before full integration and gradient verification.

If this is right

  • Gradient-based parameter estimation and sensitivity analysis become directly available for the land surface model.
  • Data assimilation tasks can use exact gradients instead of finite-difference approximations.
  • Ensemble simulations at scales of thousands of members complete in a fraction of the original wall-clock time.
  • The same pipeline can be applied to translate additional legacy Earth system model components.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The method could extend to legacy codes in other domains such as atmospheric or ocean modeling.
  • Differentiable versions of physical models may support hybrid physics-ML architectures that require end-to-end gradients.
  • The observed ensemble speedup implies practical gains for uncertainty quantification workflows that rely on large sample sizes.

Load-bearing premise

The iterative LLM compile-repair loop with the Fortran oracle will produce modules that remain numerically equivalent after full call-graph integration and during gradient computation.

What would settle it

Execute the translated JAX model on the same input sets as the original Fortran version and observe output values or computed gradients that deviate beyond floating-point tolerance.

Figures

Figures reproduced from arXiv: 2606.07681 by Aya Lahlou, Linnia Hawkins, Pierre Gentine.

Figure 2
Figure 2. Figure 2: Fortran Oracle Construction and Functional Testing Flowchart. RL refers to Ralph Loop. Dotted arrows refer to updates to the state documents. The Fortran tests are executed once under fixed inputs, sav￾ing the reference input-output pairs at each checkpoint for validation during the translation phase. 3.4. Iterative Translation, Testing, and Repair Following the bottom-up dependency order from Phase 1, eac… view at source ↗
Figure 4
Figure 4. Figure 4: Integration and Differentiability Validation Flowchart. level. Fortran DO loops over Runge-Kutta sub-steps are re￾placed with jax.lax.scan, tracing the loop body once at compile time, resulting in a single XLA kernel spanning all sub-steps. This transformation is necessary for efficient gradient computation — JAX can differentiate Python for loops by unrolling them into the computation graph, but do￾ing so… view at source ↗
Figure 3
Figure 3. Figure 3: Autonomous Agentic Translation, Testing, and Repair Flowchart. 3.5. Phase 5: Integration and Differentiability Validation Following module-level translation, an Integration Agent assembles the full column pipeline and validates end-to-end behavior against the Full column Fortran oracle as seen in figure 4. This phase revealed errors not exposed by module￾level parity tests, such as mismatched array shapes … view at source ↗
Figure 5
Figure 5. Figure 5: Oracle validation: time series (left) and scatter compari￾son (right) of JAX vs. Fortran outputs for sensible heat (H), latent heat (LE), net radiation (Rn), and GPP across 1488 half-hourly timesteps (May 2007, CHATS7). 4.2. Validation of Backpropagation Capability We validate jax.grad over the CLM-ml-jax column us￾ing central finite differences for four key parameters (leaf absorptivity αsw, Vc,max 25, st… view at source ↗
Figure 6
Figure 6. Figure 6: Jacobian-based sensitivity analysis: heatmap of ∂(GPP, H, LE)/∂θ to forcing parameters (Vc,max 25, air temper￾ature, shortwave radiation, specific humidity q, dpai (plant area index per canopy layer)), computed via jax.jacrev in one backward pass. Stomatal model: WUE. GPP, H, and LE are dpai￾weighted canopy sums of leaf-level fluxes. a) Log-scale Jacobian magnitude. b) Row-normalized relative sensitivity (… view at source ↗
Figure 8
Figure 8. Figure 8: Proof-of-concept parameter recovery for ι, Vc,max 25, and Tref (CHATS7, single timestep, May 2007). (a) Loss vs. evalu￾ations (gradient and forward-pass counts combined) for Adam+AD (blue solid), L-BFGS-B+AD (orange dash-dot), and Nelder-Mead (green dotted). L-BFGS-B+AD reaches ∼ 10−19 in < 50 eval￾uations; Nelder-Mead requires ≈ 8× more. Adam+AD stalls at ∼ 10−2 within 100 steps. (b) Parameter recovery ra… view at source ↗
Figure 7
Figure 7. Figure 7: AD vs. finite-difference timing as a function of number of parameters p (CHATS7, GPU, scalar GPP loss). Blue bars: TAD (jax.grad, constant in p). Orange bars: TFD (2p forward evaluations, linear in p). AD becomes cheaper than FD at p ≥ 3, confirming the theoretical crossover at pcross = Tb/(2Tf ) ≈ 2.2. At p = 5, AD is 2.2× faster than FD; this advantage grows linearly with p. Parameter Calibration - Proof… view at source ↗
Figure 9
Figure 9. Figure 9: Throughput scaling of CLM-ML-JAX with ensemble size N (CHATS7 walnut orchard, 46 layers, Quadro RTX 8000). N is the number of independent forward passes—each with a distinct parameter vector—run simultaneously, as needed for ensemble calibration or uncertainty quantification. (a) GPU amortized cost falls from 24.9 to 11.4 ms/sample as N grows from 1 to 2048; Fortran executes serially and stays flat at ≈54 … view at source ↗
Figure 10
Figure 10. Figure 10: CHATS7 May 1, 2007: Canopy profiles at noon (timestep 24): JAX vs. Fortran reference across all 46 canopy layers. Variables shown include air temperature, wind speed, specific humidity, CO2 concentration, and leaf-level photosynthesis and stomatal conductance. 12 [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Differentiability repair campaign timeline (April 1 – May 8, 2026, 46 sessions). Stems show bugs fixed per session. The dashed line shows the cumulative count (right axis). Background shading marks the Four dominant phases: NaN elimination (orange), zero-gradient root cause (salmon), IFT and parameter-injection fixes (blue), calibration and optimization (green). Full 7-parameter Jacobian with all non-zero… view at source ↗
read the original abstract

Differentiable programming offers transformative capabilities for scientific modeling, enabling gradient-based parameter estimation, sensitivity analysis, and data assimilation. Yet, migrating legacy codebases into differentiable frameworks remains a challenge. We present a five-phase LLM-based agentic pipeline that translates legacy Fortran into JAX: static dependency analysis determines module translation order from the full call graph; iterative compile-repair loops correct errors autonomously; and a Fortran reference oracle enforces numerical parity at the module level before integration and gradient verification. We instantiate and evaluate the pipeline on CLM-ml-v2, a 19,000-line Fortran land surface model, and analyze agent behavior across 73 module translation tasks. The resulting differentiable model computes the complete Jacobian in a single backward pass, recovers physical parameters in eight times fewer steps than gradient-free optimization, and achieves a 24 times wall-clock speedup over sequential Fortran at ensemble size N=2,048. Both the translated model and pipeline infrastructure are released as a reusable framework for differentiating other Earth system model components.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper presents a five-phase LLM-based agentic pipeline for translating legacy Fortran code to JAX, demonstrated on the 19,000-line CLM-ml-v2 land surface model across 73 modules. The pipeline performs static dependency analysis to order translations, uses iterative compile-repair loops, and applies a Fortran reference oracle for module-level numerical parity before integration and gradient verification. The authors report that the resulting differentiable model computes the full Jacobian in one backward pass, recovers physical parameters in eight times fewer optimization steps than gradient-free methods, and achieves a 24 times wall-clock speedup over sequential Fortran at ensemble size N=2,048, with both the model and pipeline infrastructure released as open artifacts.

Significance. If the numerical equivalence claims hold including for derivatives, this work offers a practical, reusable approach to converting large legacy scientific codes into differentiable form. This could enable gradient-based parameter estimation, sensitivity analysis, and data assimilation in Earth system models at scale. The explicit release of the translated model and pipeline infrastructure is a clear strength, supporting reproducibility and extension by the community.

major comments (2)
  1. [Pipeline description] Pipeline description (abstract and methods): The iterative compile-repair loop enforces numerical parity only at the per-module level with the Fortran oracle before full call-graph integration. No details are given on the gradient verification step (e.g., whether it checks derivatives via finite differences or JAX autodiff, tolerance thresholds, or handling of control-flow changes), leaving open the risk that repairs preserving scalar outputs alter associativity or evaluation order enough to change computed Jacobians. This directly underpins the single-backward-pass Jacobian, 8× optimization, and 24× speedup claims.
  2. [Results] Results (evaluation of 73 modules): The manuscript reports aggregate performance numbers but provides no per-module success/failure rates, error distributions, or ablation studies isolating pipeline components. This absence leaves the reliability of the translation process and the robustness of the headline metrics only moderately supported.
minor comments (1)
  1. [Results] A table or figure summarizing translation outcomes, repair iterations, and any residual discrepancies across the 73 modules would improve clarity and allow readers to assess scalability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback. The two major comments identify areas where the manuscript can be strengthened with additional methodological detail and granular results. We address each point below and will revise accordingly.

read point-by-point responses

  1. Referee: [Pipeline description] Pipeline description (abstract and methods): The iterative compile-repair loop enforces numerical parity only at the per-module level with the Fortran oracle before full call-graph integration. No details are given on the gradient verification step (e.g., whether it checks derivatives via finite differences or JAX autodiff, tolerance thresholds, or handling of control-flow changes), leaving open the risk that repairs preserving scalar outputs alter associativity or evaluation order enough to change computed Jacobians. This directly underpins the single-backward-pass Jacobian, 8× optimization, and 24× speedup claims.

    Authors: We agree that the gradient verification procedure requires more explicit description. The current text references the step but does not elaborate on its implementation. In the revised manuscript we will add a dedicated paragraph in the Methods section specifying that gradient verification employs JAX autodiff with cross-checks against finite-difference approximations, states the tolerance criteria used, and describes how control-flow and associativity changes are monitored during the integration phase to preserve Jacobian fidelity. revision: yes

  2. Referee: [Results] Results (evaluation of 73 modules): The manuscript reports aggregate performance numbers but provides no per-module success/failure rates, error distributions, or ablation studies isolating pipeline components. This absence leaves the reliability of the translation process and the robustness of the headline metrics only moderately supported.

    Authors: The manuscript does analyze agent behavior across the 73 tasks, yet presents outcomes in aggregate form. We acknowledge that per-module breakdowns and component ablations would provide stronger support. In revision we will add these elements, either in the main text or as supplementary material, including success/failure counts per module, error distributions for the translated modules, and an ablation isolating the contribution of the dependency-analysis and compile-repair stages. revision: yes

Circularity Check

0 steps flagged

Empirical engineering demonstration with external Fortran oracle and timing benchmarks; no derivations reduce to inputs

full rationale

The paper describes an LLM-based translation pipeline evaluated on CLM-ml-v2 via module-level numerical parity checks against a Fortran reference oracle, followed by integration, gradient verification, and empirical measurements of Jacobian computation, optimization steps, and wall-clock speedups. These outcomes are obtained by direct execution and benchmarking rather than any mathematical derivation, parameter fitting, or self-referential definition. No equations or claims reduce by construction to prior fitted values or self-citations; the central results rest on observable runtime behavior against independent external references.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The work relies on standard assumptions about LLM code generation capabilities and Fortran/JAX numerical semantics rather than introducing new free parameters, axioms, or invented entities.

pith-pipeline@v0.9.1-grok · 5717 in / 1138 out tokens · 17674 ms · 2026-06-27T23:55:46.628031+00:00 · methodology

discussion (0)

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Reference graph

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