此 MCP 可以做什么
Uses symbolic regression and SINDy to discover equations, differential equations, uncertainty intervals, and prediction bands from data.
功能
工具
4
工具
feature_request
Request a feature that Occam doesn't support yet.
Use this when you need a capability that Occam doesn't currently
offer. Requests are logged and used to prioritize development.
Rate limit: 5 requests/hour per IP, 50/hour global — stricter than
the compute tools' 10/hour to prevent log flooding. Descriptions
longer than 500 characters are truncated.
输入模式
{'type': 'object', 'title': 'request_featureArguments', 'required': ['description'], 'properties': {'description': {'type': 'string', 'title': 'Description', 'description': "A short description of the feature you need. Examples: 'LaTeX output for equations', 'support for ODE constraints', 'GPU-accelerated search', 'larger dataset limits'. Helps prioritize development."}}}
输出模式
{'type': 'object', 'title': 'FeatureRequestResult', 'required': ['ok', 'message', 'description'], 'properties': {'ok': {'type': 'boolean', 'title': 'Ok'}, 'message': {'type': 'string', 'title': 'Message'}, 'description': {'type': 'string', 'title': 'Description'}}, 'additionalProperties': False}
pysr_run
Evolutionary Symbolic Regression (PySR).
Discovers algebraic equations y = f(x1, x2, ...) from feature/target
data. Returns a Pareto front ranked by the complexity/accuracy
tradeoff. Slower than SINDy (10-60s); searches often terminate early
on convergence. For differential equations from time series, use
sindy_run instead.
Pricing: free tier up to 100 rows × 8 features, 60s timeout. Beyond
that, $0.25 + $0.03 per 100 extra rows + $0.01 per extra feature
squared, timeout up to 300s (5 min), via x402 (USDC on Base) or
MPP/Stripe. MPP/Stripe adds a flat $0.35 per-transaction fee (Stripe
processing), so the MPP challenge amount in a `payment_required`
response is $0.35 higher than the x402 amount for the same base
price; x402 gets the lower rate. Omit `payment` for free-tier
requests; paid requests without a valid credential receive a
`payment_required` result with pricing and accepted schemes. Full
pricing: occam://pricing
Advisory limits: jobs over 50,000 rows or 20 features are accepted
but may not converge; response carries a top-level `warning`.
Operators: fixed supported set only — custom operators (e.g.
'inv(x) = 1/x') are rejected. Unary: sin, cos, tan, exp, log, log2,
log10, sqrt, abs, sinh, cosh, tanh. Binary: +, -, *, /, ^.
See also prompt `supported_operators`.
Loss metric: `loss` (in `pareto_front[].loss` and `best_loss`) is
mean squared error between model prediction and `y` on the full
training set — not RMSE, and not normalized by Var(y). A threshold
appropriate for one dataset scales with y's magnitude, so set
`loss_threshold` with that in mind (e.g. for y values near 1.0,
1e-6 is a tight fit; for y near 1000, the equivalent is 1.0).
Early termination: set `loss_threshold` to stop at your noise floor.
The server also stops when the search stalls (<1% improvement in the
last third of the budget); disable with `stall_detection=false`.
Response `stop_reason` is one of: loss_threshold, stall, timeout,
natural.
If `feature_names` is supplied, its length must equal the number of
columns in `X`; a mismatch is rejected with a validation error.
Follow-up: call `pysr_uncertainty` with a chosen expression and the
same dataset for bootstrap confidence intervals on its fit constants
and optional prediction bands.
Rate limit: 10 requests/hour per IP, 200/hour global, max queue
depth 20 (shared with sindy_run and pysr_uncertainty).
Response (success) includes `pareto_front[]` (each with `complexity`,
`loss`, `expression`, `expression_latex`), `best_expression`,
`best_expression_latex`, `best_loss`, `best_complexity`, `stop_reason`,
`elapsed_seconds`, `queue_seconds` (>0 = server saturated; use as
backoff signal), optional `warning`, optional `_meta` (MPP receipt).
Full response and payment-required schemas: occam://tool-schemas
Example request:
X=[[0.0], [1.0], [2.0], [3.0], [4.0]], y=[1.0, 3.0, 5.0, 7.0, 9.0],
feature_names=["x"], max_complexity=10, timeout_seconds=15
Policy: occam://privacy-policy — Citation: occam://citation-info
只读
输入模式
{'type': 'object', 'title': 'run_pysr_toolArguments', 'required': ['X', 'y'], 'properties': {'X': {'type': 'array', 'items': {'type': 'array', 'items': {'type': 'number'}}, 'title': 'X', 'examples': [[[0.0], [1.0], [2.0], [3.0], [4.0]]], 'minItems': 5, 'description': '2D array of input features. Each row is an observation, each column is a feature. Minimum 5 rows. Free tier: 100 rows, 8 features. Paid tier: up to 50,000 rows, 20 features.'}, 'y': {'type': 'array', 'items': {'type': 'number'}, 'title': 'Y', 'examples': [[1.02, 2.97, 5.01, 7.03, 8.98]], 'minItems': 5, 'description': 'Target values, one per row of X.'}, 'payment': {'anyOf': [{'type': 'object', 'additionalProperties': True}, {'type': 'string'}, {'type': 'null'}], 'title': 'Payment', 'default': None, 'description': 'Payment credential. Accepts either a JSON object or a JSON-encoded string (FastMCP\'s transport pre-parses strings whose field annotation is non-bare-`str` into objects, so the object form is canonical; the string form is accepted for legacy callers). Required when the dataset exceeds the free tier (100 rows, 8 variables). Omit for free-tier requests. For x402: {"transaction":"0x...","network":"...","priceToken":"..."}. For MPP/Stripe: {"challenge":{...},"payload":"..."}. For prepaid API key: {"scheme":"prepaid","api_key":"occ_live_...","request_id":"<optional uuid>"}.'}, 'populations': {'type': 'integer', 'title': 'Populations', 'default': 15, 'maximum': 20, 'minimum': 1, 'description': 'Number of evolutionary populations for the search. Default 15, max 20.'}, 'feature_names': {'anyOf': [{'type': 'array', 'items': {'type': 'string'}}, {'type': 'null'}], 'title': 'Feature Names', 'default': None, 'description': 'Names for each variable/feature column. Defaults to x0, x1, ...'}, 'loss_threshold': {'anyOf': [{'type': 'number', 'exclusiveMinimum': 0}, {'type': 'null'}], 'title': 'Loss Threshold', 'default': None, 'description': 'Optional early-stop threshold on the best loss found. If set, the search terminates as soon as any Pareto-front member reaches a loss at or below this value, even if the timeout has not been reached. Useful when you know your noise floor. Default: None (no user threshold; the search runs until the stall detector or timeout).'}, 'max_complexity': {'type': 'integer', 'title': 'Max Complexity', 'default': 20, 'maximum': 25, 'minimum': 1, 'description': 'Maximum expression tree size. Higher allows more complex expressions. Default 20, max 25.'}, 'stall_detection': {'type': 'boolean', 'title': 'Stall Detection', 'default': True, 'description': 'When true (default), the server stops the search early if the best loss has not improved by more than 1% during the last third of the time budget. This reclaims compute once the search has converged. Set to false only if you want the search to run for the full timeout regardless of progress.'}, 'timeout_seconds': {'type': 'integer', 'title': 'Timeout Seconds', 'default': 60, 'maximum': 300, 'minimum': 1, 'description': 'Wall clock time limit in seconds. Free tier: max 60. Paid tier: max 300 (5 minutes). Default 60.'}, 'unary_operators': {'anyOf': [{'type': 'array', 'items': {'type': 'string'}}, {'type': 'null'}], 'title': 'Unary Operators', 'default': None, 'description': "Allowed unary operators, drawn from the fixed supported set: sin, cos, tan, exp, log, log2, log10, sqrt, abs, sinh, cosh, tanh. Custom operators (e.g. 'inv(x) = 1/x') are NOT supported — only the names listed are accepted. Default: sin, cos, exp, log, sqrt. Pass [] for none."}, 'binary_operators': {'anyOf': [{'type': 'array', 'items': {'type': 'string'}}, {'type': 'null'}], 'title': 'Binary Operators', 'default': None, 'description': 'Allowed binary operators, drawn from the fixed supported set: +, -, *, /, ^. Custom operators are NOT supported. Default: +, -, *, /. Pass [] for none.'}}}
输出模式
{'type': 'object', '$defs': {'PySRParetoEntry': {'type': 'object', 'title': 'PySRParetoEntry', 'required': ['complexity', 'loss', 'expression', 'expression_latex'], 'properties': {'loss': {'type': 'number', 'title': 'Loss'}, 'complexity': {'type': 'integer', 'title': 'Complexity'}, 'expression': {'type': 'string', 'title': 'Expression'}, 'expression_latex': {'anyOf': [{'type': 'string'}, {'type': 'null'}], 'title': 'Expression Latex'}}, 'additionalProperties': True}}, 'title': 'PySRRunResult', 'properties': {'warning': {'anyOf': [{'type': 'string'}, {'type': 'null'}], 'title': 'Warning', 'default': None}, 'best_loss': {'anyOf': [{'type': 'number'}, {'type': 'null'}], 'title': 'Best Loss', 'default': None}, 'stop_reason': {'anyOf': [{'type': 'string'}, {'type': 'null'}], 'title': 'Stop Reason', 'default': None}, 'pareto_front': {'anyOf': [{'type': 'array', 'items': {'$ref': '#/$defs/PySRParetoEntry'}}, {'type': 'null'}], 'title': 'Pareto Front', 'default': None}, 'queue_seconds': {'anyOf': [{'type': 'number'}, {'type': 'null'}], 'title': 'Queue Seconds', 'default': None}, 'best_complexity': {'anyOf': [{'type': 'integer'}, {'type': 'null'}], 'title': 'Best Complexity', 'default': None}, 'best_expression': {'anyOf': [{'type': 'string'}, {'type': 'null'}], 'title': 'Best Expression', 'default': None}, 'elapsed_seconds': {'anyOf': [{'type': 'number'}, {'type': 'null'}], 'title': 'Elapsed Seconds', 'default': None}, 'best_expression_latex': {'anyOf': [{'type': 'string'}, {'type': 'null'}], 'title': 'Best Expression Latex', 'default': None}}, 'additionalProperties': True}
pysr_uncertainty
Bootstrap confidence intervals for the numeric constants of a
frozen expression, plus optional prediction bands on an x-grid.
Typical flow: call pysr_run, pick an expression from the response
(best_expression or a pareto_front entry), pass it back here with
the same dataset to get CIs on its fit constants.
Returns frequentist bootstrap confidence intervals, not Bayesian
credible intervals — posterior inference over expression structures
is an open research problem. This tool freezes the expression
chosen by the caller and bootstraps only its numeric constants;
uncertainty about *which* expression is correct is not quantified.
Bootstrap semantics:
- If y_sigma is supplied, uses parametric bootstrap
(y_b = y + Normal(0, y_sigma)). CI reflects user-stated
measurement noise.
- Otherwise uses residual bootstrap: fit once, resample residuals.
CI reflects estimated-from-residuals noise.
Only Float constants in the expression become free parameters.
Integers stay structural (the 2 in x**2 is a function-class choice,
not a fit constant). Expressions with no Float constants
(e.g. "x + y") will be rejected with a validation error.
Expression grammar: the `expression` string is parsed by sympy.
Accepted operators are the same set pysr_run emits: unary `sin`,
`cos`, `tan`, `exp`, `log`, `log2`, `log10`, `sqrt`, `abs`, `sinh`,
`cosh`, `tanh`; binary `+`, `-`, `*`, `/`, `^` (or `**`). Whitespace
and parenthesization are free. Every free symbol in the expression
must correspond to an entry in `feature_names` — an unrecognised
symbol is silently treated as a fresh sympy Symbol and the fit will
fail downstream rather than reject early. Parse failures (syntax
errors, malformed operators) surface as tool errors.
If `feature_names` is supplied, its length must equal the number of
columns in `X`; a mismatch is rejected with a validation error.
Pricing: always free, regardless of dataset size. This tool has no
`payment` parameter and is never subject to the x402/Stripe gate.
Large bootstrap jobs still count against the shared rate limit
below, so budget `n_resamples` accordingly.
Rate limit: 10 requests/hour per IP, 200/hour global, max queue
depth 20 (shared with sindy_run and pysr_run).
只读
输入模式
{'type': 'object', 'title': 'run_pysr_uncertainty_toolArguments', 'required': ['expression', 'X', 'y'], 'properties': {'X': {'type': 'array', 'items': {'type': 'array', 'items': {'type': 'number'}}, 'title': 'X', 'examples': [[[0.0], [1.0], [2.0], [3.0], [4.0]]], 'minItems': 5, 'description': '2D array of input features. Each row is an observation, each column is a feature. Minimum 5 rows. Free tier: 100 rows, 8 features. Paid tier: up to 50,000 rows, 20 features.'}, 'y': {'type': 'array', 'items': {'type': 'number'}, 'title': 'Y', 'examples': [[1.02, 2.97, 5.01, 7.03, 8.98]], 'minItems': 5, 'description': 'Target values, one per row of X.'}, 'alpha': {'type': 'number', 'title': 'Alpha', 'default': 0.05, 'description': 'Significance level. 0.05 → 95%% CI. Default 0.05.', 'exclusiveMaximum': 1, 'exclusiveMinimum': 0}, 'x_grid': {'anyOf': [{'type': 'array', 'items': {'type': 'array', 'items': {'type': 'number'}}}, {'type': 'null'}], 'title': 'X Grid', 'default': None, 'description': 'Optional 2D grid of feature values at which to report a prediction band. Must have the same number of columns as X. Omit to skip prediction-band computation.'}, 'y_sigma': {'anyOf': [{'type': 'array', 'items': {'type': 'number'}}, {'type': 'number'}, {'type': 'null'}], 'title': 'Y Sigma', 'default': None, 'description': 'Optional per-point measurement standard deviations, or a single scalar applied to all points. When supplied, the helper uses parametric bootstrap (y_b = y + Normal(0, y_sigma)); otherwise it uses residual bootstrap. Supplying y_sigma also improves the initial weighted fit.'}, 'expression': {'type': 'string', 'title': 'Expression', 'examples': ['2.0*x0 + 1.0'], 'description': 'The expression to bootstrap, as returned by pysr_run (`best_expression` or a `pareto_front[i].expression`). Only numeric Float constants are treated as free parameters — integers in the expression (e.g. the 2 in x**2) stay structural.'}, 'n_resamples': {'type': 'integer', 'title': 'N Resamples', 'default': 100, 'maximum': 500, 'minimum': 10, 'description': 'Number of bootstrap resamples. Higher = tighter CIs, more compute. Default 100.'}, 'feature_names': {'anyOf': [{'type': 'array', 'items': {'type': 'string'}}, {'type': 'null'}], 'title': 'Feature Names', 'default': None, 'description': 'Names for each variable/feature column. Defaults to x0, x1, ...'}}}
输出模式
{'type': 'object', '$defs': {'UncertaintyCoefficient': {'type': 'object', 'title': 'UncertaintyCoefficient', 'required': ['name', 'initial', 'estimate', 'ci'], 'properties': {'ci': {'type': 'array', 'title': 'Ci', 'maxItems': 2, 'minItems': 2, 'prefixItems': [{'type': 'number'}, {'type': 'number'}]}, 'name': {'type': 'string', 'title': 'Name'}, 'initial': {'type': 'number', 'title': 'Initial'}, 'estimate': {'type': 'number', 'title': 'Estimate'}}, 'additionalProperties': True}, 'UncertaintyPredictionPoint': {'type': 'object', 'title': 'UncertaintyPredictionPoint', 'required': ['x', 'estimate', 'ci'], 'properties': {'x': {'type': 'array', 'items': {'type': 'number'}, 'title': 'X'}, 'ci': {'type': 'array', 'title': 'Ci', 'maxItems': 2, 'minItems': 2, 'prefixItems': [{'type': 'number'}, {'type': 'number'}]}, 'estimate': {'type': 'number', 'title': 'Estimate'}}, 'additionalProperties': True}}, 'title': 'PySRUncertaintyResult', 'required': ['coefficients', 'n_requested_resamples', 'n_successful_resamples', 'bootstrap_method', 'alpha', 'note'], 'properties': {'note': {'type': 'string', 'title': 'Note'}, 'alpha': {'type': 'number', 'title': 'Alpha'}, 'coefficients': {'type': 'array', 'items': {'$ref': '#/$defs/UncertaintyCoefficient'}, 'title': 'Coefficients'}, 'prediction_ci': {'anyOf': [{'type': 'array', 'items': {'$ref': '#/$defs/UncertaintyPredictionPoint'}}, {'type': 'null'}], 'title': 'Prediction Ci', 'default': None}, 'bootstrap_method': {'type': 'string', 'title': 'Bootstrap Method'}, 'n_requested_resamples': {'type': 'integer', 'title': 'N Requested Resamples'}, 'n_successful_resamples': {'type': 'integer', 'title': 'N Successful Resamples'}}, 'description': 'Always a success shape — pysr_uncertainty is never paid.', 'additionalProperties': True}
sindy_run
Sparse Identification of Nonlinear Dynamics (SINDy).
Recovers governing differential equations (dx/dt = f(x)) from time
series data. Returns human-readable sparse expressions. Fast (seconds).
For algebraic y = f(x) relationships without time structure, use
pysr_run instead.
Pricing: free tier up to 100 rows and 8 variables. Beyond that,
$0.05 + $0.01 per 100 extra rows + $0.01 per extra variable squared,
via x402 (USDC on Base) or MPP/Stripe. MPP/Stripe adds a flat $0.35
per-transaction fee (Stripe processing), so the MPP challenge amount
in a `payment_required` response is $0.35 higher than the x402 amount
for the same base price; x402 gets the lower rate. Omit `payment`
for free-tier requests; paid requests without a valid credential
receive a `payment_required` result with pricing and accepted schemes.
Full pricing table as structured JSON: occam://pricing
Advisory limits: jobs over 500,000 rows or 50 variables are accepted
but may not converge within the time budget; the response carries a
top-level `warning` the agent should surface and treat as tentative.
If `feature_names` is supplied, its length must equal the number of
data columns; a mismatch is rejected with a validation error.
Rate limit: 10 requests/hour per IP, 200/hour global, max queue
depth 20 (shared with pysr_run and pysr_uncertainty).
Response (success) includes `equations[]` (each with `variable`,
`equation`, `expression`, `expression_latex`, `r2`), `library_terms`,
`nonzero_terms`, `elapsed_seconds`, `canonical_match` (dict with
`system`, `form`, `variable_map`, `parameter_map`, `confidence` if
the discovered system matches one of Lorenz / Lotka-Volterra /
Van der Pol / Duffing; `null` otherwise), optional `warning`,
optional `_meta` (MPP receipt on paid calls). Full response and
payment-required schemas: occam://tool-schemas
Example request:
data=[[1.0, 0.0], [0.95, -0.31], [0.81, -0.59]], t=[0.0, 0.1, 0.2],
feature_names=["x", "y"], poly_degree=2, threshold=0.1
Policy: occam://privacy-policy — Citation: occam://citation-info
只读
幂等
输入模式
{'type': 'object', 'title': 'run_sindy_toolArguments', 'required': ['data', 't'], 'properties': {'t': {'type': 'array', 'items': {'type': 'number'}, 'title': 'T', 'examples': [[0.0, 0.3, 0.6, 0.9, 1.2, 1.5, 1.8, 2.1, 2.4, 2.7, 3.0, 3.3]], 'minItems': 3, 'description': 'Timestamps corresponding to each row of data. Length must match row count.'}, 'data': {'type': 'array', 'items': {'type': 'array', 'items': {'type': 'number'}}, 'title': 'Data', 'examples': [[[1.0, 0.0], [0.9553, -0.2955], [0.8253, -0.5646], [0.6216, -0.7833], [0.3624, -0.932], [0.0707, -0.9975], [-0.2272, -0.9738], [-0.5048, -0.8632], [-0.7374, -0.6755], [-0.9041, -0.4274], [-0.99, -0.1411], [-0.9875, 0.1577]]], 'minItems': 3, 'description': '2D array of time series data. Each row is a timestep, each column is a state variable. Minimum 3 rows (finite-difference derivative). Free tier: 100 rows, 8 variables. Paid tier: up to 500,000 rows, 50 variables.'}, 'payment': {'anyOf': [{'type': 'object', 'additionalProperties': True}, {'type': 'string'}, {'type': 'null'}], 'title': 'Payment', 'default': None, 'description': 'Payment credential. Accepts either a JSON object or a JSON-encoded string (FastMCP\'s transport pre-parses strings whose field annotation is non-bare-`str` into objects, so the object form is canonical; the string form is accepted for legacy callers). Required when the dataset exceeds the free tier (100 rows, 8 variables). Omit for free-tier requests. For x402: {"transaction":"0x...","network":"...","priceToken":"..."}. For MPP/Stripe: {"challenge":{...},"payload":"..."}. For prepaid API key: {"scheme":"prepaid","api_key":"occ_live_...","request_id":"<optional uuid>"}.'}, 'max_iter': {'type': 'integer', 'title': 'Max Iter', 'default': 20, 'maximum': 100, 'minimum': 1, 'description': 'Maximum STLSQ optimizer iterations. Default 20.'}, 'threshold': {'type': 'number', 'title': 'Threshold', 'default': 0.1, 'description': 'STLSQ sparsity threshold. Higher values produce sparser equations. Default 0.1.', 'exclusiveMinimum': 0}, 'poly_degree': {'type': 'integer', 'title': 'Poly Degree', 'default': 2, 'maximum': 5, 'minimum': 1, 'description': 'Polynomial library degree for SINDy candidate functions. Default 2.'}, 'feature_names': {'anyOf': [{'type': 'array', 'items': {'type': 'string'}}, {'type': 'null'}], 'title': 'Feature Names', 'default': None, 'description': 'Names for each variable/feature column. Defaults to x0, x1, ...'}}}
输出模式
{'type': 'object', '$defs': {'SindyEquation': {'type': 'object', 'title': 'SindyEquation', 'required': ['variable', 'equation', 'expression', 'expression_latex', 'r2'], 'properties': {'r2': {'type': 'number', 'title': 'R2'}, 'equation': {'type': 'string', 'title': 'Equation'}, 'variable': {'type': 'string', 'title': 'Variable'}, 'expression': {'type': 'string', 'title': 'Expression'}, 'expression_latex': {'anyOf': [{'type': 'string'}, {'type': 'null'}], 'title': 'Expression Latex'}}, 'additionalProperties': True}, 'CanonicalMatch': {'type': 'object', 'title': 'CanonicalMatch', 'required': ['system', 'form', 'variable_map', 'parameter_map', 'confidence'], 'properties': {'form': {'type': 'string', 'title': 'Form'}, 'system': {'type': 'string', 'title': 'System'}, 'confidence': {'type': 'number', 'title': 'Confidence'}, 'variable_map': {'type': 'object', 'title': 'Variable Map', 'additionalProperties': {'type': 'string'}}, 'parameter_map': {'type': 'object', 'title': 'Parameter Map', 'additionalProperties': {'type': 'number'}}}, 'additionalProperties': True}}, 'title': 'SindyRunResult', 'properties': {'warning': {'anyOf': [{'type': 'string'}, {'type': 'null'}], 'title': 'Warning', 'default': None}, 'equations': {'anyOf': [{'type': 'array', 'items': {'$ref': '#/$defs/SindyEquation'}}, {'type': 'null'}], 'title': 'Equations', 'default': None}, 'library_terms': {'anyOf': [{'type': 'array', 'items': {'type': 'string'}}, {'type': 'null'}], 'title': 'Library Terms', 'default': None}, 'nonzero_terms': {'anyOf': [{'type': 'integer'}, {'type': 'null'}], 'title': 'Nonzero Terms', 'default': None}, 'canonical_match': {'anyOf': [{'$ref': '#/$defs/CanonicalMatch'}, {'type': 'null'}], 'default': None}, 'elapsed_seconds': {'anyOf': [{'type': 'number'}, {'type': 'null'}], 'title': 'Elapsed Seconds', 'default': None}}, 'additionalProperties': True}
历史
近期工具变更
已更改
pysr_uncertainty
2026年9月25日 02:50
已更改
pysr_run
2026年9月25日 02:50
已更改
sindy_run
2026年9月25日 02:50
已添加
pysr_uncertainty
2026年9月17日 12:39
已添加
pysr_run
2026年9月17日 12:39
已添加
sindy_run
2026年9月17日 12:39
已添加
feature_request
2026年9月17日 12:39
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