Diff Studio

Diff Studio is a package for the Datagrok platform. It provides in-browser tools for solving initial value problem for systems of ordinary differential equations (ODE) and its interactive exploration.

• Go to Apps > Compute and run Diff Studio
• Enter formulas or modify template
• Run computations and explore your model

The solver takes a set of the differential equations in a declarative form, and creates a UI that solves the equations, visualizes the results, and lets you change parameters on the fly.

Quick start

Datagrok provides intuitive tools for the rapid solving ODEs.

• Launch Diff Studio:
  • Go to Apps > Compute and run Diff Studio
  • The Hub opens with ready-to-run models grouped into Templates, Library and Recent
• Run a model:
  • Double-click any card on the Hub to run it
  • Or click Create to start from a basic template
  • Or click Upload to load an ivp-file from your disk
  • Or drag an ivp-file right into the browser
  • Modify inputs and explore computations
• Modify equations:
  • Turn on the Edit toggle on the top panel
  • Edit formulas or add new ones
  • Click Refresh or press F5 to apply changes
• Save model:
  • Click the Save button on the top panel to save model to your platform files (Browse > Files > My files)
  • Click Download to save model to a local file. Find the ivp-file in Downloads. You can open and edit this file using any text editor
  • Click Save to Library to publish the model to your personal Library — it appears on the Hub and in the browse tree
• Reopen a model:
  • Pick it from the Hub (Templates, Library, Recent) — double-click the card
  • Or use the browse tree: Browse > Apps > Compute > Diff Studio > Templates | Library | Recent
  • Or use the Open menu on the top panel — it also exposes Import... and My Models
• Analyze model
  • Turn off the Edit toggle on the top panel
  • Click the Fit icon to optimize inputs
  • Click the Sensitivity icon to run sensitivity analysis

Hub

The Hub is the default landing view of Diff Studio. It shows all available models as cards and exposes the most common actions.

• Action buttons at the top:
  • Refresh — reload the Hub contents
  • Create — start a new model from the basic template
  • Upload — load a local ivp-file and run it
• Card sections:
  • Templates — starter models (Basic, Advanced, Extended)
  • Library — built-in use cases plus models you have saved to your personal Library
  • Recent — models you have opened recently, including custom files
• Card interactions:
  • Hover a card for a tooltip with the model description
  • Double-click a card to run the model
  • Right-click a card for a context menu: Run, Copy link, Help. Custom Library cards also expose Settings... for editing the help link

The same sections are mirrored in the browse tree under Browse > Apps > Compute > Diff Studio.

Create model from template

Start from one of these templates:

| Template | Features| |----------|---------| | Basic | the simplest model| | Advanced | extra math features, including expressions, constants, parameters and tolerance specification| | Extended | the annotating feature for extended UI generation |

Library

The Library section on the Hub contains built-in example models. You can run them directly from Hub cards or from the browse tree, and use them as a starting point — they cover the main features of Diff Studio.

• Chem reactions
  • simulates mass-action kinetics
  • illustrates annotation of inputs
• Robertson's model
  • Robertson's chemical reaction model
  • stiff equations example
  • shows how Datagrok solves complicated ODEs
• Lotka-Volterra
  • classic predator-prey model
  • illustrates a small non-stiff system with interacting species
• Fermentation
  • models the kinetics of the biochemical reactions in fermentation
  • shows the usage of min and max in inputs annotation
• PK
  • pharmacokinetic (PK) simulation
  • demonstrates the usage of the meta.solver feature for numerical solver management
• PK-PD
  • simulates pharmacokinetics (PK), pharmacodynamics (PD), and their relationship
  • illustrates the usage of the loop feature for dosing specification
• Acid production
  • models gluconic acid production by Aspergillus niger
  • shows the usage of the update feature for multi-stage simulation
• Nimotuzumab
  • models population pharmacokinetic for nimotuzumab
  • demonstrates the output feature
• Bioreactor
  • simulates the bioreactor processes
  • shows how to use meta.inputs to specify a table with pre-defined model inputs
• Pollution
  • describes a chemical reaction part of the air pollution model consisting of 25 reaction and 20 reacting compounds
  • demonstrates the simulation of processes described by a stiff system of ODEs

Custom models

You can extend the Library with your own models:

• Open or write a model in the editor, then click Save to Library on the top panel. The file is stored under System:AppData/DiffStudio/library and registered in the Library manifest (external-models.json).
• The saved model appears on the Hub in the Library section and in Browse > Apps > Compute > Diff Studio > Library.
• Right-click a custom model card and choose Settings... to set a help link for it.

Datagrok's ODEs suite has tools for solving both stiff and non-stiff equations. It provides a numerical solution. The primary solvers are CVODE and LSODA — variable-order methods that automatically detect stiffness and switch between Adams (non-stiff) and BDF (stiff) formulations.

Model structure

A model defines initial value problem. It contains name, differential equations, initial values and argument specifications:

#name: My ODEs
#equations:
  dx/dt = x + y + exp(t)
  dy/dt = x - y - cos(t)
#argument: t
  initial = 0
  final = 1
  step = 0.01
#inits:
  x = 2
  y = 5

Use the following sections to specify various problems:

|Control block|Features| |-------------|--------| |#name|Defines a name| |#equations|Differential equation specification| |#argument|Independent variable specification| |#inits|Initial values specification| |#constants|Constants specification| |#parameters|Parameters specification| |#expressions|Defines auxiliary compuations| |#output|Defines output columns and their captions| |#description|Defines description of the model| |#comment|Specifies comments block| |#meta.solver|Defines the solver settings| |#meta.inputs|Path to the table with pre-defined model inputs|

Annotations

The Run tab of Diff Studio provides UI for interactive model exploration. Use annotations to improve usability. Append them, when defining parameters, initial values and argument.

Group inputs by specifying their category:

#parameters:
  P1 = 1 {category: Parameters}
  P2 = -1 {category: Parameters}

Define the desired caption:

#argument: t
  start = 0 {caption: Initial; category: Time}
  finish = 2 {caption: Final; category: Time}
  step = 0.01 {caption: Step; category: Time}

Specify min, max and step values to get sliders and clickers for the rapid model exploration:

#inits:
  x = 2 {min: 0; max: 5}
  y = 0 {min: -2; max: 2; step: 0.1}

Provide hints in brackets [ ]:

  P1 = 1 {category: Parameters} [P1 parameter tooltip]

Solver management

You can manage the solver of ODEs. Specify its settings in the #meta.solver-line:

• the numerical method (method)
• the maximum number of iterations (maxIterations)
• the maximum computation time (maxTimeMs)

Diff Studio implements the following numerical methods for solving ODEs:

Automatic stiffness-detecting methods:

|Method|Value| |-------------|--------| |CVODE - variable-order, variable-step BDF solver from SUNDIALS (Hindmarsh et al., 2005; Cohen & Hindmarsh, 1996)|'cvode'| |LSODA - variable-order solver with automatic switching between Adams (non-stiff) and BDF (stiff)|'lsoda'|

Implicit methods (for stiff ODEs) - Rosenbrock-Wanner type:

|Method|Value| |-------------|--------| |the modified Rosenbrock triple (MRT)|'mrt'| |the ROS3PRw method|'ros3prw'| |the ROS34PRw method|'ros34prw'|

Explicit methods (for non-stiff ODEs) - Runge-Kutta type:

|Method|Value| |-------------|--------| |the Bogacki-Shampine 3(2) method (RK3)|'rk3'| |the Runge-Kutta-Fehlberg 4(5) method (RK4)|'rk4'| |the Dormand-Prince 5(4) method (RKDP)|'rkdp'|

Explicit methods (for non-stiff ODEs) - Adams-Bashforth type:

|Method|Value| |-------------|--------| |the predictor-corrector method of order 4 (AB4)|'ab4'| |the predictor-corrector method of order 5 (AB5)|'ab5'|

By default, Diff Studio uses ROS34PRw. You may specify the method as follows:

#meta.solver: {method: 'cvode'}

To check correctness of formulas, set the maximum number of iterations:

#meta.solver: {method: 'mrt'; maxIterations: 1}

Diff Studio alerts you if computations take too long. The default time limit is 5 seconds. To customize it, set the maximum computation time (in milliseconds):

#meta.solver: {method: 'mrt'; maxTimeMs: 50}

Lookup tables

Lookup tables are pre-defined sets of model input values. They're organized as follows:

||x|y|...| |-----|-----|-----|---| |Set 1|1|2|...| |Set 2|3|4|...|

To use a lookup table:

• Create a CSV file with your table and add it to your project
• Add the #meta.inputs-line to your model and specify a CSV file with a lookup table
• To improve usability, define caption, category and a tooltip:

#meta.inputs: table {choices: OpenFile("System:AppData/DiffStudio/inputs.csv"); caption: Mode; category: Settings} [Hint]

Performance

Diff Studio solvers ensure fast in-browser intergration of ODEs. The following classic problems illustrate their efficiency:

• Rober
  • a stiff system of 3 nonlinear ODEs
  • describes the kinetics of an autocatalytic reaction given by Robertson
• HIRES
  • a stiff system of 8 non-linear equations
  • explains the `High Irradiance Responses' (HIRES) of photomorphogenesis on the basis of phytochrome, by means of a chemical reaction involving eight reactants
• VDPOL
  • a system of 2 ODEs proposed by B. van der Pol
  • describes the behaviour of nonlinear vacuum tube circuits
• OREGO
  • a stiff system of 3 non-linear equations
  • simulates Belousov-Zhabotinskii reaction
• E5
  • a stiff system of 4 non-linear ODEs
  • represents a chemical pyrolysis model
• Pollution
  • a stiff system of 20 non-linear equations
  • describes a chemical reaction part of the air pollution model designed at The Dutch National Institute of Public Health and Environmental Protection

The LSODA, CVODE, MRT, ROS3PRw and ROS34PRw methods demonstrate the following time performance (AMD Ryzen 5 5600H 3.30 GHz CPU):

|Problem|Segment|Points|Tolerance|LSODA, ms|CVODE, ms|MRT, ms|ROS3PRw, ms|ROS34PRw, ms| |-|-|-|-|-|-|-|-|-| |Rober|[0, 10E+11]|40K|1E-7|67|85|175|446|285| |HIRES|[0, 321.8122]|32K|1E-10|125|142|122|362|215| |VDPOL|[0, 2000]|20K|1E-12|268|352|492|1576|760| |OREGO|[0, 360]|36K|1E-8|76|98|205|483|199| |E5|[0, 10E+13]|40K|1E-6|7|*|6|17|8| |Pollution|[0, 60]|30K|1E-6|12|15|18|50|23|

* E5 is skipped for CVODE: the extremely stiff rate constants (spanning 20 orders of magnitude) cause convergence failures with the dense direct linear solver.

This table compares the efficiency of the methods when solving each test problem on a fixed segment and providing solutions at a specified number of points with a given tolerance.

Platform applications

Once you are satisfied with the result, click Save to Library on the top panel to publish your model to the Library. It becomes available on the Hub and in Browse > Apps > Compute > Diff Studio > Library for yourself and anyone with access to your files.

You can export your model to JavaScript script. To do so:

1. Turn on the Edit toggle on the top panel
2. Click </> icon. Script editor opens in a new view
3. Click SAVE button
4. Script is created, and can be found in the "Scripts" section of the platform

Apply scripting tools to get:

• non-elementary and special functions' use
• Datagrok packages' functions call

Export to LaTeX and Markdown

Diff Studio can render a model as LaTeX or Markdown for use in papers, reports and notebooks. Click the Export icon on the top panel to open the export dialog. In the dialog:

• pick the output Format:
  • latex — generates a .tex source. Toggle Standalone to wrap the output with \documentclass{article} and the required \usepackage lines so the file compiles with pdflatex out of the box
  • markdown — generates a .md file with LaTeX math blocks, suitable for GitHub, Jupyter, or static-site generators
• review the result in a live preview with syntax highlighting that follows the selected format
• toggle which sections to include (title & description, initial conditions, parameters, constants)
• enable Compact mode for small models (no section headings, inline initial conditions)
• choose between \cdot and juxtaposition for multiplication
• Copy the source to the clipboard or Download it as a file

Citation

If you use this library for research purposes, please cite the following papers:

• Diff Studio: Ecosystem for Interactive Modeling by Ordinary Differential Equations in Journal of Open Source Software (2026).

@article{diffstudio2026joss,
  title = {Diff Studio: Ecosystem for Interactive Modeling by Ordinary Differential Equations},
  author = {Viktor Makarichev, Larisa Bankurova, Gennadii Zakharov, Leonid Stolbov, Steven Mehrman, Dan Skatov, Jeffrey Cohen, Paul Sass, Davit Rizhinashvili, Andrew Skalkin},
  journal = {Journal of Open Source Software},
  year = {2026},
  volume = {11},
  number = {120},
  doi = {10.21105/joss.09090}
}

• Diff Studio: Web-Based Environment for Interactive Modeling with Ordinary Differential Equations in Springer, CoMeSySo 2025 Proceedings (Lecture Notes in Networks and Systems, vol. 1901) - foundational paper.

@InProceedings{diffstudio2026lnns,
title = {Diff Studio: Web-Based Environment for Interactive Modeling with Ordinary Differential Equations},
author = {Viktor Makarichev, Larisa Bankurova, Gennadii Zakharov, Leonid Stolbov, Steven Mehrman, Dan Skatov, Jeffrey Cohen, Paul Sass, Davit Rizhinashvili, Andrew Skalkin},
editor = {Radek Silhavy, Petr Silhavy},
booktitle = {Focus on Artificial Intelligence in Intelligent Systems Design},
year = {2026},
publisher = {Springer Nature Switzerland},
address = {Cham},
pages = {390--401},
doi = {10.1007/978-3-032-22236-7_31}
}

Links

Run Diff Studio online here, or complete an interactive tutorial. Find more features in Diff Studio docs.

See also

• Sensitivity analysis
• Parameter optimization
• Community