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‎Benchmark-Models/Ko_NeurIPS2023/README.md‎

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# Ko_NeurIPS2023
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A second-order inspired neural ordinary differential equation (neural ODE) model of
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double-pendulum dynamics [1].
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## Implementation details
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The implementation follows the double-pendulum benchmark from the original publication, with
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two differences.
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First, a 70/30 split is used for training and validation data instead of the 50/50 split
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used in the original study, as the latter led to non-correlation between training and
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validation loss.
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Second, the original publication scales the time span by the maximum training time. This
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scaling is implemented directly in the PEtab measurement tables. For example, the final
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training time point is 1.0.
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## Other notes
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Both training and validation data are provided. The corresponding PEtab-SciML problems can
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be built using the respective YAML files.
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The provided nominal values do not correspond to an optimal fit, so lower loss values can be
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achieved when training the model.
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## References
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1. Ko, Joon-Hyuk, et al. "Homotopy-based training of neuralodes for accurate dynamics
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discovery." _Advances in Neural Information Processing Systems_ 36 (2023): 64725-64752.

‎Benchmark-Models/Ko_NeurIPS2023/expected_Ko_NeurIPS2023.yaml‎

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llh:
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training: -740.8365268083237
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validation: -271.75114583603334

‎Benchmark-Models/Ko_NeurIPS2023/hybridization_Ko_NeurIPS2023.tsv‎

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targetId targetValue
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net1_input1 theta1
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net1_input2 theta2
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net1_input3 omega1
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net1_input4 omega2
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acceleration1 net1_output1
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acceleration2 net1_output2

‎Benchmark-Models/Ko_NeurIPS2023/mapping_Ko_NeurIPS2023.tsv‎

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petabEntityId modelEntityId
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net1_input1 net1.inputs[0][0]
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net1_input2 net1.inputs[0][1]
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net1_input3 net1.inputs[0][2]
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net1_input4 net1.inputs[0][3]
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net1_output1 net1.outputs[0][0]
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net1_output2 net1.outputs[0][1]
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net1_ps net1.parameters

‎Benchmark-Models/Ko_NeurIPS2023/measurements_train_Ko_NeurIPS2023.tsv‎

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‎Benchmark-Models/Ko_NeurIPS2023/measurements_validation_Ko_NeurIPS2023.tsv‎

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‎Benchmark-Models/Ko_NeurIPS2023/model_Ko_NeurIPS2023.xml‎

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<?xml version="1.0" encoding="UTF-8"?>
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<sbml xmlns="http://www.sbml.org/sbml/level3/version2/core"
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level="3"
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version="2">
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<model id="Ko_NeurIPS2023"
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name="Ko_NeurIPS2023"
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timeUnits="second">
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<notes>
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<body xmlns="http://www.w3.org/1999/xhtml">
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<p>
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Second-order neural ODE model of double-pendulum dynamics, based on
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Ko et al., NeurIPS 2023. The angular accelerations are supplied by
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the neural-network outputs through the PEtab-SciML hybridization table.
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</p>
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</body>
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</notes>
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<annotation>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
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xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
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<rdf:Description rdf:about="#Ko_NeurIPS2023">
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<bqmodel:isDescribedBy>
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<rdf:Bag>
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<rdf:li rdf:resource="https://openreview.net/forum?id=rUFckPrzXR"/>
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</rdf:Bag>
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</bqmodel:isDescribedBy>
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</rdf:Description>
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</rdf:RDF>
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</annotation>
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<listOfUnitDefinitions>
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<unitDefinition id="per_second2" name="per second squared">
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<listOfUnits>
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<unit kind="second" exponent="-2" scale="0" multiplier="1"/>
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</listOfUnits>
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</unitDefinition>
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</listOfUnitDefinitions>
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<listOfParameters>
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<parameter id="theta1"
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name="theta1"
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value="-1.1336150169372559"
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units="dimensionless"
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constant="false"/>
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<parameter id="theta2"
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name="theta2"
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value="-1.3008047342300415"
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units="dimensionless"
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constant="false"/>
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<parameter id="omega1"
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name="omega1"
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value="-0.5385388135910034"
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units="dimensionless"
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constant="false"/>
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<parameter id="omega2"
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name="omega2"
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value="-6.1550583839416495"
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units="dimensionless"
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constant="false"/>
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<parameter id="acceleration1"
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name="neural_network_angular_acceleration_1"
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units="per_second2"
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constant="true"/>
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<parameter id="acceleration2"
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name="neural_network_angular_acceleration_2"
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units="per_second2"
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constant="true"/>
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</listOfParameters>
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<listOfRules>
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<rateRule variable="theta1">
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<math xmlns="http://www.w3.org/1998/Math/MathML">
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<ci> omega1 </ci>
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</math>
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</rateRule>
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<rateRule variable="theta2">
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<math xmlns="http://www.w3.org/1998/Math/MathML">
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<ci> omega2 </ci>
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</math>
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</rateRule>
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<rateRule variable="omega1">
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<math xmlns="http://www.w3.org/1998/Math/MathML">
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<ci> acceleration1 </ci>
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</math>
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</rateRule>
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<rateRule variable="omega2">
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<math xmlns="http://www.w3.org/1998/Math/MathML">
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<ci> acceleration2 </ci>
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</math>
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</rateRule>
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</listOfRules>
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</sbml>

‎Benchmark-Models/Ko_NeurIPS2023/net1_Ko_NeurIPS2023.yaml‎

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nn_model_id: net1
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inputs:
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- input_id: input
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layers:
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- layer_id: layer1
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layer_type: Linear
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args:
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in_features: 4
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out_features: 50
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bias: true
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- layer_id: layer2
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layer_type: Linear
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args:
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in_features: 50
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out_features: 50
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bias: true
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- layer_id: layer3
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layer_type: Linear
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args:
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in_features: 50
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out_features: 2
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bias: true
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forward:
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- name: input_1
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op: placeholder
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target: input
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args: []
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kwargs: {}
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- name: layer1
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op: call_module
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target: layer1
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args:
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- input_1
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kwargs: {}
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- name: gelu
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op: call_function
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target: gelu
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args:
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- layer1
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kwargs:
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inplace: false
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- name: layer2
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op: call_module
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target: layer2
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args:
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- gelu
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kwargs: {}
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- name: gelu_1
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op: call_function
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target: gelu
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args:
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- layer2
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kwargs:
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inplace: false
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- name: layer3
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op: call_module
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target: layer3
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args:
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- gelu_1
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kwargs: {}
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- name: output
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op: output
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target: output
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args:
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- layer3
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kwargs: {}

‎Benchmark-Models/Ko_NeurIPS2023/observables_Ko_NeurIPS2023.tsv‎

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observableId observableFormula noiseFormula noiseDistribution
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obs_theta1 theta1 1 normal
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obs_theta2 theta2 1 normal
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obs_omega1 omega1 1 normal
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obs_omega2 omega2 1 normal

‎Benchmark-Models/Ko_NeurIPS2023/parameters_Ko_NeurIPS2023.tsv‎

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parameterId lowerBound upperBound nominalValue estimate
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net1_ps -Inf Inf array true

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