Inverse Intelligence Group

We turn forward models upside down

If you cannot clearly assign the cause to measured data, then you are dealing with inverse problems. Our team of experts in physics and data science can help: Using invertible neural networks and scientific AI, we turn your measurement noise into understandable parameters and simulations into predictive sensors.

We make ambiguous measurement and process data from industrial plants finally analyzable - through the development and integration of AI solutions. Our open VIPR Inversion Engine delivers Bayesian inference/inversion, uncertainty quantification, virtual sensing, real-time alerting, and fully integrable REST interfaces – production-ready, transparent, and modularly extensible. We combine physical understanding, scientific machine learning, and productive implementation to help industrial companies and applied research institutions gain robust insights and control logic from the most complex data.

Inverse problems we have solved

VIPR - Versatile Framework for Inverse Problems

The Problem: Reconstruction of hidden material properties from complex measurement data

Illustration showing the operation of GIWAXS (Grazing-Incidence Wide-Angle X-Ray Scattering). On the left, a schematic representation shows how a grazing-incidence X-ray beam strikes a thin organic layer and produces a two-dimensional GIWAXS scattering pattern. Above this, a typical molecular motif with characteristic spacings is shown. The central GIWAXS image displays circular or semi-circular reflection patterns resulting from the periodic arrangement of molecules. On the right, measured GIWAXS profiles and atomic structural models illustrate different crystalline orientations and lattice planes. The reflection rings in the 2D scattering patterns correspond to the shown lattice planes and enable conclusions about the molecular arrangement within the layer. Source: Arora et al., Science 358 (6364), 2017.

Working with the neutron reflectometer creates a physically demanding inverse problem: from noisy reflectivity measurement data, central material properties such as layer thickness, roughness, or density profiles must be reconstructed. Together with MLZ Instrument Scientist Dr. Alexandros Koutsiumpas, the entire measurement and analysis process was examined. The challenge is to read the machine's data almost in real-time, automatically select the appropriate pre-trained model from metadata, and reliably feed the analysis results back into the experimental workflow – for example, for in-situ machine control. At the same time, the results should be visualized in an understandable and user-friendly way via a frontend.

The Solution Approach: Invertible neural networks for fast and robust reconstructions

The figure first shows that direct problems enable unambiguous mapping from inputs to outputs, while inverse problems often have multiple possible solutions. The lower diagram explains how an invertible neural network (INN) handles such ambiguous backward problems: The INN maps inputs to outputs in the forward process and uses L2 norm to fit training data. For the inverse direction, the model combines the output with an additional latent variable that is fitted to a normal distribution using maximum mean discrepancy, allowing reconstruction of the original inputs. Source: Ardizzone et al., ICLR 2019.

An invertible neural network enables direct solution of the inverse problem: it learns the mapping between measurement data and material properties in a way that this relationship remains unique and reversible. This allows the model to directly infer the underlying material parameters from noisy reflectivity curves – without time-consuming iterative simulations. Through automated selection of a suitable, pre-trained model, new measurement data can be analyzed immediately, while the web interface allows even non-specialists to intuitively experiment with different models and compare their results.

The Result: Dramatic acceleration and better usability in the research process

The figure shows the graphical user interface of the VIPR framework, where individual processing steps such as data loading, model loading, normalization, preprocessing, prediction, and postprocessing can be configured. On the right is the graphical output of a calculated reflectivity curve, where measured and predicted data are almost perfectly aligned. Below the graph, the automatically determined layer parameters of a polymer film are listed, including thickness, scattering length density, and the very short execution time of 0.95 seconds. Comparison with a classical iterative evaluation method shows an acceleration of approximately 195-fold. Source for classical approach: Analakasis, J. Appl. Cryst. (2021), 54, 1857–1866.

This approach achieved a 195-fold acceleration: analysis time dropped from around 185 seconds to about 1 second – fast enough for real-time applications. The results can be immediately fed into automated workflows, allowing machines to be dynamically adjusted during measurement. At the same time, the intuitive web visualization ensures that both experts and non-specialists can efficiently evaluate the data and immediately assess measurement quality. This creates a powerful and practical solution that demonstrates how modern invertible neural networks can solve complex technical challenges in practice.

Services

We develop complete AI-based analysis and process intelligence for industrial measurement systems:

Bayesian Inference & INNs

Development, training, and adaptation of invertible models for layer thicknesses, material parameters, plasma states, sensor drifts, and other ambiguous measurement processes.

Data Strategy & Data Acquisition

Planning and construction of data pipelines, data models, data collection, robustification, and automated data management.

Synthetic Data & Simulation

Generation of training data using physical models or generative models – ideal when data is scarce or expensive.

VIPR Integration

Implementation of a modular analysis and control pipeline based on our open-source VIPR framework. With REST API, plug-ins, alerting, and dashboards.

Product Integration

Seamless integration into existing systems, measurement device software, automation systems, or edge infrastructure.

Interested?

Our Working Method

  1. Problem Definition and Domain Analysis

    • Formulation of the inverse or data-driven problem in physical context
    • Analysis of relevant mechanisms, boundary conditions, and measurement chains
    • Identification of reconstructable quantities and necessary diagnostics
  2. Data Acquisition and Preliminary Analysis

    • Structured recording of measurement, process, and metadata
    • Synchronization, filtering, calibration, and quality checking
    • Extraction of physically significant features and time regimes
  3. Design of Inversion Model and Training

    • Selection of suitable model architecture (e.g., Invertible Neural Network, Physics-informed Neural Network, Bayesian Inference)
    • Integration of physical constraints and process knowledge
    • Training with real, synthetic, or hybrid datasets, possibly on high-performance computers
  4. System Integration and API Deployment

    • Provision of the model as a scalable API or edge component
    • Connection to measurement systems, controls, and data services
    • Secure operation via REST, gRPC, or OPC-UA
  5. Validation and Pilot Operation

    • Experimental verification of reconstructions and predictions
    • Analysis of uncertainties, robustness, and real-time capability
    • Iterative adjustment based on pilot data and expert feedback
  6. Production Deployment and Lifecycle Support

    • Deployment in target environment with monitoring and versioning
    • Continuous model monitoring, drift detection, and re-training
    • Technical support, documentation, and continuous optimization

We are more than just another AI agency

We are not just an AI agency on cloud nine. We are physicists, machine learning engineers, scientists, innovators, and we work in a practical manner. We combine science-driven AI with a deep understanding of processes and systems. With open frameworks like our VIPR Inversion Stack, Bayesian inference, physics-informed neural networks, and normalizing flows, we build transparent, auditable, and industry-ready pipelines that seamlessly link measurement data, simulations, and automation systems. This creates solutions that enable robust state reconstructions, secure process control, and scalable integrations, far beyond what traditional AI agencies deliver.

What Distinguishes Us

Scientific Machine Learning

We develop science-driven AI models that explicitly consider physical laws, nonlinearities, and uncertainties. Our focus is on physics-informed neural networks, normalizing flows (INN/cINN), and hybrid models that combine data and process knowledge. This allows us to derive robust state reconstructions and process predictions from limited or noisy measurement data.

Bayesian Inference

For inverse problems, we use Bayesian inversion methods and invertible neural networks to determine latent states from observable effects – including uncertainty quantification. This approach allows proper treatment of ambiguous measurement situations, incorporation of prior knowledge, and statistically validated reconstruction of solution spaces. Our methods are applied where classical optimization fails or physical models are incomplete.

Understanding Complex Systems

Our team of physicists and computer scientists analyzes systems with many coupled mechanisms, nonlinear feedbacks, and emergent behavior. Whether plasma, coating, or measurement processes: we model the underlying structures in latent state space and make their dynamics quantifiable. This allows us to visualize stability limits, transition regimes, drift phenomena, and process hysteresis – and make them usable for data-driven optimization.

Open Source Frameworks

Our tools are based on open, transparent frameworks such as PyTorch or VIPR, deployed in large research facilities like MLZ. We develop modular pipelines for data acquisition, analysis, inversion, and visualization – fully traceable and extensible. Open source creates trust, facilitates audits, and enables long-term maintainability in industrial applications.

Measurement and Automation Technology

We integrate AI models into industrial measurement and automation systems. This includes:

  • Multi-sensor fusion
  • Real-time state reconstruction
  • REST and edge deployments
  • Feedback to control systems

We connect modern AI with proven measurement technology and automation to make processes more robust, adaptive, and predictable.

Ready to take the first step?

Contact us now and we will find the right solution for your requirements!