| Algorithm | llm4ed |
|---|---|
| Dataset | llm4ed-heat |
| Expression | \( u_{t} = 0.05014 u_{xx} \) |
| Best LLM4ED sparse reward | 0.9889 |
| R² | 0.999999 |
| NMSE | 1.198e-06 |
| Iterations | 12 |
| Early Stopped | False |
| config.algorithm | llm4ed |
| config.temperature | 0.8 |
| config.max_tokens | 1024 |
| config.stop_threshold | 0.995 |
| config.reward_limit | 0.5 |
| config.pool_size | 5 |
| config.init_num | 20 |
| config.samples_per_epoch | 8 |
| config.max_llm_calls_per_propose | 6 |
| config.max_llm_calls_per_run | 200 |
| config.seed | 42 |
| config.model | nvidia/llama-3.3-nemotron-super-49b-v1.5 |
| config.base_url | https://integrate.api.nvidia.com/v1 |
| config.tape_record_path | None |
| config.provider_kind | finite_diff |
Read the best native score reached at each search iteration.
Compare predicted and observed targets against the diagonal of exact agreement.
Read the published equation with its fitted coefficients and active terms.
Read the operators and derivatives that compose the published equation.
Read the distribution and spatial pattern of predicted minus observed target values.
Compare the magnitudes and signs of the active fitted coefficients.
Compare the measured field with forward integration of the discovered equation and their difference.
Compare the fitted derivative target with the equation prediction and their residual, without forward integration.
Compare measured and integrated fields at the labeled observation times.
Locate the signed field error from forward integration at the labeled physical coordinates.
Elite-pool reward band (best / median / worst) per round -- pool quality and diversity as the LLM proposer evolves.
Number of invalid scoring events per round (n_invalid): parse / solve failures across all resamples. Rising counts flag the LLM proposing more unusable equations.
Total provider completions issued through each round (running sum of per-round n_llm_calls) -- the search's whole-run budget spend.
{
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"best_expression": "u_xx + u * u_x ",
"best_score": 0.9889,
"iterations": 12,
"early_stopped": false,
"final_eval": {
"mse": 2.820049985269267e-09,
"nmse": 1.1975145765820022e-06,
"r2": 0.9999988024854234,
"score": 0.9889,
"complexity": 1,
"coefficients": [
0.05013629421591759,
0.0
],
"is_valid": true,
"error_message": "",
"invalid_reason": null,
"selected_indices": [
0
],
"residuals": "[40200 elements]",
"terms": [
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],
"expression": "u_xx + u * u_x ",
"lhs_name": "u_t",
"condition_number": null,
"condition_number_computed": false
},
"actual": "[40200 elements]",
"predicted": "[40200 elements]",
"dataset_name": "llm4ed-heat",
"algorithm_name": "Llm4edPlugin",
"config": {
"algorithm": "llm4ed",
"temperature": 0.8,
"max_tokens": 1024,
"stop_threshold": 0.995,
"reward_limit": 0.5,
"pool_size": 5,
"init_num": 20,
"samples_per_epoch": 8,
"max_llm_calls_per_propose": 6,
"max_llm_calls_per_run": 200,
"seed": 42,
"model": "nvidia/llama-3.3-nemotron-super-49b-v1.5",
"base_url": "https://integrate.api.nvidia.com/v1",
"tape_record_path": null,
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},
"recorder": {
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0.9889,
0.9889,
0.9889,
0.9889,
0.9889,
0.9889,
0.9889,
0.9889,
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0.9889
],
"pool_median": [
0.6815,
0.8548,
0.8548,
0.8605,
0.8605,
0.8605,
0.8605,
0.8605,
0.8605,
0.9124,
0.9124,
0.9124
],
"pool_worst": [
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],
"n_invalid": [
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"n_llm_calls": [
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4,
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2,
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2,
3,
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6,
2
],
"n_valid": [
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8,
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0,
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8,
8,
6,
8
],
"n_invalid_undefined_operands": [
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0,
0,
0,
0,
0,
0,
0,
1,
0,
0,
0
],
"n_invalid_undefined_operators": [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
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],
"n_invalid_inexpressible": [
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"n_invalid_parse": [
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"n_invalid_non_finite": [
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"n_invalid_lstsq": [
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"n_invalid_abnormal_coef": [
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"n_invalid_other": [
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"_best_expr": [
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"u_xx + u * u_x ",
"u_xx + u * u_x ",
"u_xx + u * u_x ",
"u_xx + u * u_x ",
"u_xx + u * u_x ",
"u_xx + u * u_x ",
"u_xx + u * u_x ",
"u_xx + u * u_x ",
"u_xx + u * u_x ",
"u_xx + u * u_x ",
"u_xx + u * u_x "
],
"_n_candidates": [
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8,
8,
8,
0,
8,
4,
8,
8,
8,
6,
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]
},
"lhs_label": "u_t",
"equation": {
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},
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]
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"attrs": null,
"active_indices": [
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},
"manifest": {
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"kd_version": "0.7.5",
"seed": 42,
"terms": null,
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"resumed": false,
"resume_source": null
},
"run_record": {
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"evidence_hash_scheme": "kd-evidence-v1",
"created_at": "2026-09-14T04:34:33+00:00",
"cost": {
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"search_seconds": 70.23656755499542,
"boundary_results": 82,
"boundary_invalid_results": 0,
"preprocessing_seconds": 0.008415824035182595,
"surrogate_train_seconds": null,
"cpu_seconds": 70.193541,
"tokens_in": 18283,
"tokens_out": 17955,
"tokens_cached": null,
"api_cost_usd": null
},
"evidence": {
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"expression": "u_xx + u * u_x ",
"score_kind": "LLM4ED sparse reward",
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"headline_coefficient_source": "native",
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"mse": 2.820049985269267e-09,
"nmse": 1.1975145765820022e-06,
"r2": 0.9999988024854234,
"score": 0.9889,
"residual_stats": {
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}