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PDE-Controller: LLMs for Autoformalization and Reasoning of PDEs

T0 review · 3 major / 4 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read Fine-tuned LLMs autoformalize plain-English PDE control problems, write solver code, and propose subgoal constraints, improving utility gain by up to 62% over GPT-4o.

desk verdict A substantial dataset and trained pipeline for NL-to-STL PDE control, but the 62% utility-gain headline collapses in the paper's own end-to-end table. read the letter →

arxiv 2502.00963 v2 pith:OPLUZDTW submitted 2025-02-03 cs.LG

Mauricio Soroco , Jialin Song , Mengzhou Xia , Kye Emond , Weiran Sun , Wuyang Chen This is my paper · ORCID
classification cs.LG MSC 68T5068T0793C2035K0535L05
keywords PDEcontrolsignaltemporallogicautoformalizationreasoningprogramsynthesisheatequationwavedirectpreferenceoptimization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that large language models can take plain-English descriptions of PDE control problems and handle the whole pipeline: formalizing constraints, writing solver code, and reasoning about how to control the system better. Its three fine-tuned components — a Translator that converts natural language into Signal Temporal Logic (STL), a Coder that writes Python for the Gurobi MILP solver, and a Controller trained by DPO to propose intermediate subgoal specifications — are trained on a released dataset of over two million synthetic 1D heat- and wave-equation problems. On synthetic benchmarks the Controller raises the utility gain for heat control by 62% over GPT-4o ($\Delta r = 1.453$ vs $0.897$), with 0.992 IoU autoformalization and 0.998 code executability; on 34 human-written problems the Translator's IoU drops to about 0.71 (heat) and no model produces valid reasoning subgoals. The authors frame the work as a first testbed for LLMs in applied mathematics and release data, code, and checkpoints.

What carries the argument

The load-bearing object is the subgoal STL $\phi'$: a Signal Temporal Logic formula — a spatiotemporal constraint of the form $G_{[t_1,t_2]}(\forall x \in [x_1,x_2]: u(x) \lessgtr ax+b)$ or its $F$ ('eventually') variant — whose continuous semantics assign a real utility $r(\phi)$ via min/max over the constraint's space-time region. The reasoning mechanism is sequential two-stage optimization: solve $\phi'$ with Gurobi (capped at 120 seconds), use the resulting field as the new initial condition for the anchor $\phi$, and record $r(\phi|\phi')$; the Controller LLM is trained with DPO on win/lose pairs of subgoals labeled by whether $r(\phi|\phi') > r(\phi)$, regularized by an SFT term so it keeps producing valid STL syntax. This converts the non-convex MILP of direct control into a learned warm-start search over initial conditions.

What would settle it

A concrete experiment: measure the valid-subgoal rate and mean utility gain $\Delta r$ of the released Controller on the 34 human-written problems with the authors' parsing tool. The paper reports this value is effectively zero for every model; if it stays zero when the base model is scaled up or the prompt format changes, the 62% utility-gain claim is a property of the synthetic distribution, not of PDE control generally.

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Extended reading notes

Core claim

The paper's central claim is that a fine-tuned LLM can improve open-loop PDE control by decomposing the target specification into a subgoal: for an anchor STL $\phi$, the Controller proposes a subgoal $\phi'$, the system optimizes $\phi'$ first, adopts the reached state as the new initial condition, and then optimizes $\phi$, scoring the pair as $r(\phi|\phi')$ against the direct-solve utility $r(\phi)$. The authors report that heat problems reach a success rate of 0.812 and a mean utility gain of $\Delta r = 1.453$, a 62% improvement over GPT-4o's $0.897$, and that the full pipeline — Translator, Coder, Controller — handles synthetic autoformalization at 0.992 IoU and code executability at 0.998. On the 34 human-written problems, the Translator's IoU drops to about 0.71 (heat) and no model, including PDE-Controller, produces valid reasoning subgoals, which the authors attribute to unstructured phrasing, inconsistent units, and unfamiliar notation in the manual data.

Load-bearing premise

The reported gains assume that the synthetic problem distribution — hand-picked STL templates with sampled parameters, solved through Gurobi's MILP formulation of the discretized heat and wave equations — faithfully represents real PDE control quality; the authors' own manual test set strains this assumption, with Translator IoU dropping from 0.992 to 0.711 (heat) and no model generating valid reasoning subgoals on manual problems.

Editorial extensions

If this is right

  • A fine-tuned 7B open-weights checkpoint can exceed prompted frontier models specifically on PDE-control formalization and reasoning: the Translator reaches 0.992 IoU on synthetic problems and the Controller produces valid subgoal STLs at 82.7%, while GPT o1-mini yields essentially no valid subgoal STLs on the synthetic benchmark.
  • The components compose end-to-end: feeding the Translator's noisy STL predictions into the Coder costs only 0.57% additional utility RMSE, so autoformalization errors are largely absorbed by the code generator.
  • The subgoal-reasoning skill transfers to unseen 4-constraint STL formats (IoU 0.934–1.0), suggesting the learned subgoal prior generalizes beyond the 1–3 constraint training distribution.
  • The gains are strongest for heat problems ($\Delta r = 1.453$, +62% over GPT-4o's 0.897); wave gains are smaller, and no model improves the hardest wave anchors.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The Controller's subgoal proposal is effectively a learned warm-start for a non-convex MILP; replacing the Gurobi solver with a differentiable physics surrogate would allow the subgoal to be trained end-to-end on gradient signals rather than win/lose labels, a path the paper does not take.
  • Because the preference labels are computed purely from the utility $r(\phi|\phi')$, the same DPO recipe transfers to other objectives — such as control-input energy, tracking error, or satisfaction margin — without changing the framework.
  • The manual-data failure suggests the reported gains are tied to the synthetic templates' parameter ranges and phrasing; a direct check is whether fine-tuning on human-written problems, or augmenting templates with the observed manual defects (mixed units, 'ho' for rho, missing material data), restores valid subgoal proposals.
  • The framework is limited to open-loop control; extending the Controller's proposals to a receding-horizon, closed-loop scheme would test whether the learned subgoal distribution remains useful when re-planning from feedback states.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper presents PDE-Controller, a fine-tuned LLM framework for 1D heat- and wave-equation control. The pipeline has three trained components: a Translator (natural language to Signal Temporal Logic), a Controller (proposes intermediate subgoal STLs, trained with DPO), and a Coder (STL to Python/Gurobi code). Training uses a synthetically generated dataset of roughly 2.13 million (NL, STL, Python) triplets, plus 34 manually written problems. The authors report strong synthetic performance for autoformalization (IoU 0.992), program synthesis (executability up to 0.9978), and reasoning, including a headline "up to 62% improvement in utility gain" on heat problems. The central utility-gain claim, however, comes from a decoupled evaluation in which generated subgoal STLs are paired with ground-truth Python code, and the paper's own end-to-end evaluation reports a negative average utility gain on heat problems for the full pipeline.

Significance. If the end-to-end utility gains were real, this would be a substantial contribution: it would demonstrate a trained LLM pipeline capable of formalizing informal PDE control tasks and improving open-loop control quality through subgoal reasoning, backed by a large released dataset and reproducible model checkpoints. The Translator and Coder results on synthetic data are strong, and the decoupled reasoning evaluation is a useful methodological contribution. However, the headline claim is not supported by the deployed system: Table 17 shows heat All Δr = -0.731 for the full pipeline, and on wave problems the proposed Controller trails GPT-4o in end-to-end utility gain. The significance of the paper is therefore conditional on either repairing the end-to-end gap or explicitly re-scoping all utility-improvement claims to the oracle-code setting.

major comments (3)
  1. [Abstract; Section 4.2; Table 9; Table 17] The central claim of improved PDE control utility is internally inconsistent with the paper's own end-to-end results. The abstract and Section 4.2 advertise "up to 62% improvement in utility gain" based on Table 9, but footnote 5 states that this evaluation provides true Python code for any valid generated subgoal STL. When the full pipeline is run end-to-end (Table 17), the same Controller achieves heat All Δr = -0.731, meaning subgoal reasoning degrades utility relative to direct solving, and on wave All the proposed model's Δr = 0.698 is below GPT-4o's 0.778. The claim that PDE-Controller "improves the utility of PDE control" is therefore not supported for the actual deployed system; it holds only in the decoupled oracle-code setting. The authors must either provide an end-to-end evaluation supporting the claim, or re-scope the abstract and Section 4.2 to state explicitly that utility improvements apply only when the Coder's output is replaced by ground-truth code.
  2. [Table 9; Table 18; Section 4.2] The baseline comparison in the decoupled reasoning evaluation is difficult to interpret because nearly all baseline subgoal STLs are invalid. Table 9 reports valid STL rates of 82.70% for Ours, 42.45% for MathCoder2, 2.55% for GPT-4o, and 0.04% for GPT-o1-mini, and Table 18 gives per-difficulty proportions of valid ϕ′ as low as 0.008 for GPT-4o on wave problems. Since Success Rate P and Utility Gain Δr are computed only over proposed subgoal STLs that are syntactically valid, the GPT baselines contribute only a handful of samples to their Δr estimates; the claim that GPT-4o is the "second-best" with Δr = 0.897 on heat rests on an extremely small valid subset. The authors should report the number of valid proposals per model and difficulty level, and should also present a comparison in which invalid proposals are explicitly counted as failures (e.g., zero utility or a penalty), otherwise the headline improvement over GPT models in reasoning is not robustly established.
  3. [Section 4.2; Table 5; Table 16; Appendix D] The paper's applicability to real-world problems is materially narrower than the abstract suggests. Section 4.2 states that on manual data all models fail to generate meaningful reasoning steps due to invalid subgoal STL proposals, and Table 5 shows Translator IoU dropping from 0.992 on synthetic heat data to 0.711 on manual heat data, while Table 16 shows end-to-end heat executability dropping to 0.451 for Ours. The claims of PDE reasoning and utility gains should be explicitly restricted to the synthetic template distribution defined in Section 3.2 and Tables 12-13, with a clear statement that the manual evaluation covers only autoformalization and program synthesis, not the reasoning/utility contribution. The abstract and contribution list currently overstate the framework's real-world behavior.
minor comments (4)
  1. [Table 4; Table 5] The parenthetical deviations in Tables 4 and 5 are unclear: for example, IoU = 0.992 with a reported deviation of 0.07 appears inconsistent with a metric bounded in [0,1], and the same applies to IoU = 0.772 with deviation 0.35. Please clarify whether these are standard deviations, standard errors, or percentages of some quantity.
  2. [Table 3; Appendix A.4] The metric name "Utility RMSE" is described as "Relative mean square error" in the footnote to Table 3, which mixes RMSE and relative-error terminology. Please use one consistent definition and state the exact formula.
  3. [Tables 9, 17, 18, 19] The column header "Math-Coderv2" appears with a typo in several tables; it should read "MathCoder2".
  4. [Section 3.2; Appendix H.2] The claim that this is the "first comprehensive dataset" for PDE control should be tempered, since the synthetic portion is generated from 1374 hand-designed STL templates over two PDE types with fixed parametric ranges; the manual portion has only 34 samples. Some statement of coverage limitations would be more appropriate than "comprehensive".

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the PDE-Controller pipeline is trained and evaluated on externally computed solver utilities, and its claimed gains do not reduce to the training labels by construction.

full rationale

The paper's derivation chain is self-contained rather than circular. The utility r(phi) is defined by STL continuous semantics (Appendix A.2, Eqs. 7-12) and computed by an external MILP solver (Gurobi) after FEM discretization (Appendix A.3), so the evaluation metric is not a fitted constant of the LLMs. The Controller's DPO training uses preference pairs labeled by r(phi|phi') > r(phi) (Sec. 3.4.2), and the same utility difference is used at test time to define P and Delta r (Sec. 4.2); this is standard RLHF/RL practice, not a construction-level equivalence, because the held-out test problems and generations are not the training pairs and the model can fail to improve utility (as it does for hard wave problems and in end-to-end Table 17). The decoupled reasoning evaluation in Table 9, which supplies true Python code for valid generated subgoal STLs (footnote 5), is an explicit ablation that isolates the Controller from Coder errors; the contradiction with the end-to-end numbers in Table 17 (heat All Delta r = -0.731) is an internal-consistency and overclaiming concern, not circularity, because no equation or fitted parameter is being renamed as a prediction. The paper also states that on manually written data all models fail to generate meaningful reasoning steps; that is an external-validity limitation, not a circular step. No load-bearing self-citations or imported uniqueness theorems appear in the argument.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The framework rests on a chain of domain assumptions inherited from STL and MILP control literature plus hand-chosen synthetic data ranges. None of these are derived in the paper; they define what 'utility' and 'success' mean, so they carry much of the evidentiary load.

free parameters (5)
  • Subgoal time placement rule = subgoal interval must precede anchor interval within global tmax
    Design choice in Sec 3.4.1 restricting the STL search space; all reasoning results depend on it.
  • Difficulty-level thresholds (P thresholds) = Heat: Easy (0.8,1], Medium (0.5,0.8], Hard [0,0.5]; Wave: Easy (0.88,1], Medium (0.55,0.88], Hard [0,0.55]
    Chosen in Table 8 to balance problem counts across levels; reported performance is averaged within these hand-set bins.
  • Dataset hyperparameter ranges = e.g., L in [50,300] mm, temp in [250,350] K, tmax in [5,15] s, a in [-0.5,0.5], b in temp+[-20,20], kappa in…
    Hand-specified sampling ranges in Tables 12-13 define the entire synthetic distribution on which all models are trained and evaluated; they are free choices by the authors.
  • Solver timeout for subgoal STL = 120 seconds (Gurobi)
    Footnote in Sec 3.4.1: runtime threshold for solving phi'; affects which subgoals are considered successful.
  • Paraphrase count for NL augmentation = 5 paraphrases per problem via GPT-4o-mini
    Sec 3.2; affects diversity of natural language inputs and distribution shift to manual data.
assumptions (5)
  • domain assumption FEM discretization and MILP relaxation faithfully represent the PDE control problem (Appendix A.3).
    The entire utility computation and subgoal evaluation rely on the equivalence stated in Sec 2.3 and A.3, taken from Sadraddini and Belta (2015) and Alvarez (2020), not re-derived here.
  • domain assumption The STL continuous semantics r(phi) (Appendix A.2) is the correct quantitative measure of PDE constraint satisfaction.
    All reported gains in utility are differences of r(phi); the metric is inherited from prior STL control literature.
  • ad hoc to paper Subgoal decomposition improves open-loop PDE control utility (Sec 3.4.1).
    The paper hypothesizes this based on robotics subgoal works; it is not proven and Table 17 shows it can fail.
  • ad hoc to paper The synthetic dataset distribution (template STLs, Tables 12-13 ranges, GPT paraphrase) is representative of real PDE control problems.
    Manual data results are substantially worse (IoU 0.65-0.71 vs 0.992 synthetic), showing a distribution gap; the model's high synthetic scores do not transfer.
  • domain assumption Gurobi solves the discretized MILP accurately within the 120-second time limit, so r(phi) is a trustworthy number.
    All utility labels and evaluation metrics are Gurobi outputs; the paper provides no verification of optimality gaps.

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Cite this review

Pith. "Pith review of PDE-Controller: LLMs for Autoformalization and Reasoning of PDEs." pith.science (2026). https://pith.science/paper/OPLUZDTW

@misc{pith2026250200963,
  author       = {Pith},
  title        = {Pith review of: PDE-Controller: LLMs for Autoformalization and Reasoning of PDEs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OPLUZDTW}},
  note         = {Machine review of arXiv:2502.00963}
}
read the original abstract

While recent AI-for-math has made strides in pure mathematics, areas of applied mathematics, particularly PDEs, remain underexplored despite their significant real-world applications. We present PDE-Controller, a framework that enables large language models (LLMs) to control systems governed by partial differential equations (PDEs). Our approach enables LLMs to transform informal natural language instructions into formal specifications, and then execute reasoning and planning steps to improve the utility of PDE control. We build a holistic solution comprising datasets (both human-written cases and 2 million synthetic samples), math-reasoning models, and novel evaluation metrics, all of which require significant effort. Our PDE-Controller significantly outperforms prompting the latest open source and GPT models in reasoning, autoformalization, and program synthesis, achieving up to a 62% improvement in utility gain for PDE control. By bridging the gap between language generation and PDE systems, we demonstrate the potential of LLMs in addressing complex scientific and engineering challenges. We release all data, model checkpoints, and code at https://pde-controller.github.io/.

Figures

Figures reproduced from arXiv: 2502.00963 by the authors.

Figure 1
Figure 1. We build LLMs for automated, accelerated PDE control. significant weaknesses in complex domains. LLMs strug￾gle with precise mathematical reasoning (Mirzadeh et al., 2024; Feng et al., 2024; Ahn et al., 2024), understanding nuanced constraints (Williams & Huckle, 2024), or making decisions grounded in physical-world consequences (Wang et al., 2024; Jia et al., 2024; Cheng et al., 2024). Addressing these limitations … view at source ↗
Figure 2
Figure 2. PDE control adjusts inputs (heat, force) to ensure sys￾tems (modeled by PDEs) satisfy spatiotemporal constraints. 2. Preliminaries 2.1. Background of PDE Control Partial differential equations (PDEs) model nearly all of the physical systems and processes of interest to scientists and engineers. PDE control involves adjusting external inputs like heat or force to guide a system governed by physical laws (PDEs) to mee… view at source ↗
Figure 3
Figure 3. Overview of our PDE-Controller framework. The Translator directly autoformalizes an informal PDE control problem ( yellow ) into formal specifications with STL ( blue ). The Controller proposes novel STL subgoals ( purple ). Each STL is synthesized into specialized Python programs by the Coder ( green ) and optimized externally (white). From the initial condition (i.), our PDE reasoning optimizes a subgoal (ii.) bef… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Workflow for supervised fine-tuning (SFT) of autoformalization (Translator LLM) and program synthesis (Coder LLM). Note that the utility is only used for evaluation and not used for SFT. Without reasoning, the Translator and Coder try to faithfully and directly solve t…
Figure 5
Figure 5. Figure 5: Learning PDE control reasoning via RLHF. Given the input prompt, our Controller LLM trained with preference data via reinforcement learning, will propose a subgoal STL ϕ ′ . From the initial condition u (0), the PDE system is controlled by ϕ ′ to reach state u ′ , and …
Figure 6
Figure 6. Figure 6: Case study of LLM reasoning for PDE control on heat (top) and wave (bottom) problems (symbols are aligned with [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: Case study of heat problems with different difficulty levels: easy (top), medium (middle), hard (bottom). Symbols are aligned with [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 8
Figure 8. Figure 8: Case study of wave problems with different difficulty levels: easy (top), medium (middle), hard (bottom). Symbols are aligned with [PITH_FULL_IMAGE:figures/full_fig_p017_8.png]
Figure 9
Figure 9. Figure 9: Synthesized control inputs for the heat (top) and the wave (bottom) problems in Fig.6. Left: Solution for directly solving ϕ. Right: Solution for solving ϕ based on subgoal ϕ ′ , where red vertical dashes indicate the control shift from ϕ ′ to ϕ [PITH_FULL_IMAGE:figur…
Figure 10
Figure 10. Figure 10: Google Form for collecting manually written PDE control problems. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_10.png]
Figure 11
Figure 11. Figure 11: Background of our questionnaire participants. E. Training Details We leverage the pretrained MathCoder2-DeepSeekMath-7B (Lu et al., 2024) checkpoint (MathCoder2) which has a 4096- token context length. All our trained models are evaluated zero-shot. For fair compariso…

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Reinforcement Learning with Verifiable Physics: Post-training LLMs with Continuous Rewards

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    RLVP post-trains one LLM across eight PDE families with hybrid validity-plus-continuous physics rewards, improving solver accuracy and enabling selective compositional transfer to held-out PDEs.

Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages · cited by 1 Pith paper

  1. [1]

    The purpose is to reduce the second-order derivatives of u to first derivatives so that we can obtain (linear) approximations to u

    The PDE is converted into its weak (variational) form by integrating against suitable test functions v(x). The purpose is to reduce the second-order derivatives of u to first derivatives so that we can obtain (linear) approximations to u. This also simplifies boundary condition handling and smoothness requirements in the original PDE. 13

    work page

  2. [2]

    The spatial domain of the PDE’s weak form is discretized by dividing it into small, simple geometric elements (intervals in 1D, triangles/quadrilaterals in 2D; tetrahedra in 3D), essentially forming a mesh, and choosing local basis functions on each element

    work page

  3. [3]

    The stiffness matrix (K) and mass matrix (M) encode the PDE’s structure

    Contributions from local (spatial) elements are assembled across the entire mesh into a global linear system, often written as M ˙˜u + K ˜u = F . The stiffness matrix (K) and mass matrix (M) encode the PDE’s structure. The banded stiffness matrix (K) arises from terms involving derivatives (e.g.,∇u · ∇v in the weak form). The diagonal mass matrix (M) come...

    work page

  4. [4]

    average@k

    The temporal domain is further discretized using finite difference schemes, obtaining a set of difference equations that must be solved at each time step. This final step produces the final linear (or nonlinear) system of equations that is solved numerically to approximate the solution of the original PDE. M ˜un+1 − ˜un ∆t + K ˜un+1 = F n+1. (13) This can...

    work page 2024

  5. [5]

    Easy: Anchor Constraints STL (ϕ): F[1.17,3.48](∀x ∈ [10, 25](u(x) − (−0.2169 · x + 286.5171) > 0))∧ (G[4.64,5.13](∀x ∈ [41, 55](u(x) − (−0.2225 · x + 311.8826) < 0))∨ F[6.04,11.77](∀x ∈ [61, 89](u(x) − (0.0988 · x + 310.7904) > 0))) Subgoal STL Proposal (ϕ′) by Controller: F[0.42,0.99](∀x ∈ [10, 25](u(x) − (−0.2907 · x + 323.3970) > 0))∧ (G[0.10,0.57](∀x ...

    work page

  6. [6]

    Medium: Anchor Constraints STL (ϕ): G[2.18,2.70](∀x ∈ [0, 30](u(x) − (0.4159 · x + 293.2549) > 0))∨ (G[4.03,7.79](∀x ∈ [46, 63](u(x) − (−0.0956 · x + 296.0596) < 0))∧ F[8.33,13.41](∀x ∈ [75, 96](u(x) − (0.2602 · x + 309.7111) > 0))) Subgoal STL Proposal (ϕ′) by Controller: G[0.66,1.68](∀x ∈ [0, 30](u(x) − (0.3616 · x + 387.4454) > 0))∨ (G[0.52,2.03](∀x ∈ ...

    work page

  7. [7]

    Wave We show easy/medium/hard problems in Fig

    Hard: Anchor Constraints STL (ϕ): G[2.62,4.50](∀x ∈ [22, 87](u(x) − (−0.0122 · x + 294.2976) > 0)) Subgoal STL Proposal (ϕ′) by Controller: G[1.29,2.50](∀x ∈ [22, 87](u(x) − (−0.0157 · x + 408.1535) > 0)) B.2. Wave We show easy/medium/hard problems in Fig. 8, with their anchor STL (ϕ) and subgoal STL (ϕ′) listed below

    work page

  8. [8]

    Hard Figure 8: Case study of wave problems with different difficulty levels: easy (top), medium (middle), hard (bottom)

    Easy: Anchor Constraints STL (ϕ): (G[0.25,0.54](∀x ∈ [7207, 23479](u(x) − (2.2684e − 05 · x + 1.4129) < 0))∧ F[0.76,0.84](∀x ∈ [42469, 65095](u(x) − (1.8952e − 06 · x − 1.7928) > 0)))∨ F[1.12,1.33](∀x ∈ [77653, 85444](u(x) − (−4.0675e − 05 · x + 2.1560) > 0)) Subgoal STL Proposal (ϕ′) by Controller: (G[0.10,0.24](∀x ∈ [7207, 23479](u(x) − (3.0242e − 05 · ...

    work page 1961

Show all 16 references
  1. [9]

    Medium: Anchor Constraints STL (ϕ): G[0.10,0.24](∀x ∈ [13787, 21080](u(x) − (−9.5400e − 06 · x − 0.3744) < 0))∨ F[0.05,0.09](∀x ∈ [49923, 59039](u(x) − (1.2003e − 05 · x − 1.5231) > 0))∨ G[0.78,1.31](∀x ∈ [78762, 86964](u(x) − (4.3983e − 05 · x − 1.5994) > 0)) Subgoal STL Prop...

  2. [10]

    for one point during

    Hard: Anchor Constraints STL (ϕ): (G[0.23,0.30](∀x ∈ [12400, 20684](u(x) − (4.0369e − 05 · x − 0.9002) > 0))∧ F[0.72,0.82](∀x ∈ [33059, 46052](u(x) − (3.5491e − 07 · x − 1.4933) < 0)))∨ F[1.10,1.11](∀x ∈ [67963, 79313](u(x) − (1.6090e − 06 · x − 1.1675) > 0)) 17 Subgoal STL Pr...

    2023

  3. [11]

    At a specific moment within the time period [t0] to [t1], the temperature distribution along the rod must exceed the linear profile mu0(x) = [a0] * x + [b0] in the segment defined by [r0] and [r1]

  4. [12]

    Within the time frame of [t0] to [t1], there should be at least one instance where the rod’s temperature distribution surpasses the linear profile mu0(x) = [a0] * x + [b0] from [r0] to [r1]

  5. [13]

    During the interval between [t0] and [t1], there is a moment at which the temperature across the rod must be greater than the linear profile mu0(x) = [a0] * x + [b0] within the range of [r0] and [r1]

  6. [14]

    Throughout the duration from [t0] to [t1], there exists a point in time where the temperature distribution of the rod should be greater than the linear profile mu0(x) = [a0] * x + [b0] applicable between the sections [r0] and [r1]

  7. [15]

    ho” instead of “rho

    At some time during the interval between [t0] and [t1], it is required that the temperature distribution of the rod exceeds the linear profile mu0(x) = [a0] * x + [b0] in the region from [r0] to [r1]. Table 14 shows the character-level relative edit distance between each natur...

  8. [2023]

    raw” data saved in addition to the preprocessed/cleaned/labeled data (e.g., to support unanticipated future uses)? If so, please provide a link or other access point to the “raw

    enable task-specific translations from informal language to Linear Temporal Logic (LTL), allowing robots to follow structured plans even in low-resource scenarios. Building on this foundation, recent research has explored the use of LLMs for task planning, demonstrating models...

    2023

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