Modelling the real world: reliably and at scale.

We design and implement quantitative models and software tools to simulate complex systems. Whether you're capturing physical processes, engineered systems, or data-driven phenomena, our models are grounded in first principles and enhanced by data.

We specialize in PDE-based modeling and simulation, with expertise in scalable implementations using tools like FEniCS (finite elements), OpenFOAM (finite volumes), and custom solvers. Our work spans deterministic and stochastic systems, hybrid physics-ML architectures, and multiscale formulations.

From early-stage prototyping to production-scale simulation, we support the full modeling lifecycle by delivering actionable insight across domains and deployment environments.

Turning Scientific Data into Predictive Power.

From physical measurements to simulation outputs, scientific data is everywhere but traditional models often struggle. They may oversimplify complex dynamics or demand excessive compute. We address this by building custom machine learning tools tailored to your scientific workflows.

Our approach draws on scientific machine learning (SciML), where first-principles physics meets data-driven modeling. Whether you're accelerating a numerical solver, constructing a digital twin, or learning unknown dynamics from experiments, we develop models that are accurate, efficient, and physically grounded.

Use cases include building foundation models, design optimization, and uncertainty quantification: all powered by modern ML for science.

Solvers that fit your problem, not the other way around.

At Open Numerics we have decades of experience designing state-of-the-art numerical and machine learning algorithms for scientific and engineering applications. We specialize in creating methods that are tightly aligned with the structure and demands of your problem, not some generic off-the-shelf tools.

Our expertise spans fast linear and nonlinear solvers, domain-specific PDE discretizations, adaptive time-stepping, and particle-based simulation methods. We also build scalable surrogate models, customized ML optimizers, advanced sampling techniques, and uncertainty quantification workflows for both deterministic and stochastic systems.

From multiscale dynamics to PDE-constrained optimization, we develop robust computational tools that enable deeper insight and better performance, all grounded in scientific rigor and algorithmic innovation.

Predictions without uncertainty are incomplete.

We go beyond point estimates to deliver confidence. We specialize in quantifying how much trust you can place in your numerical models and machine learning predictions. Using advanced techniques in Bayesian inference, stochastic sampling, and uncertainty quantification, we help you capture uncertainty from parameter calibration to predictive distributions.

Our methods go beyond in-sample fit, addressing out-of-sample generalization and rare-event analysis. Whether you're solving PDEs with uncertain inputs or deploying ML models in high-risk settings, our probabilistic approach delivers predictions that are robust, transparent, and decision-ready.

Speed is strategy.

In modern computational science and machine learning, performance isn't optional - it's foundational. At Open Numerics, we help you unlock the full power of your hardware by accelerating your models and simulations with GPU computing, CUDA programming, and high-performance computing (HPC) techniques.

From custom CUDA kernels and GPU-enabled machine learning to parallel solvers and large-scale simulation pipelines, we optimize your code to make the most of modern architectures. Whether you're handling terabytes of data, simulating PDEs at scale, or deploying ML workflows using Slurm, we create solutions tailored for performance, efficiency, and scalability.

Seamless deployment, your way.

We don't just build models, we help you integrate them into your workflow. Whether you need an onsite installation, a private cloud setup, or a lightweight containerized service, we deliver solutions where and how you need them.

Our deployment support spans everything from local execution to scalable hosted platforms. We work closely with your team to ensure smooth integration with your existing systems, whether you're running simulations, launching ML services, or automating pipelines. Flexibility is built into every step so our tools are ready to deliver value from day one.