INGUZ NAVITASPhysics-Informed AI Discuss your process
PINN · Digital Twins · Predictive Control

Physics where data ends. Prediction before the deviation.

We build Physics-Informed Neural Networks that fuse governing physical laws with process data — fast, predictive models of complex industrial systems.

measurement→state estimation→prediction→optimization→control
Explore the technology Read the research
Digital Twins Model Predictive Control State Estimation Anomaly Detection Edge AI
How it works

One closed loop, six steps.

Watch a measurement travel the predictive control loop — from the physical plant, through the PINN digital twin, to the action applied back on the process.

01 / 06

Physical system

The real plant runs — temperatures, pressures and flows evolve continuously in real time.

T · P · ṁ · Y · X · Q
02 / 06

Sensors & data

Sensors sample the process; the raw data is acquired, cleaned and normalized.

→ data → x(t)
03 / 06

PINN digital twin

The physics-informed twin estimates the full state — including variables the sensors can't measure.

y = fθ(x, t, p)
04 / 06

State prediction

The twin projects the process forward in time for each candidate control action.

x(t + τ)
05 / 06

Optimization

Each scenario is scored against the objective; the best action is selected.

u* = arg min J(u)
06 / 06

Predictive control

The chosen action is applied — before a deviation occurs. Then the loop repeats.

apply u* → process → repeat
01 / 06
The shift

From reacting to a deviation
to predicting the process.

Traditional control responds to a deviation that has already occurred. Predictive control evaluates the expected future behaviour of the process and acts before an undesirable state is reached.

◦ Reactive control
Measurement
Deviation estimation
Control action
● Predictive control
Measurementx(t)
State estimation
Process predictionx(t+τ)
Optimizationmin J
Control actionu*
Technology

A neural network that obeys physics.

A Physics-Informed Neural Network incorporates the governing physical laws directly into the learning process. It is trained not only to fit data, but to satisfy the differential equations, initial conditions and boundary conditions that describe the process.

Eq. 4
Physics-informed loss
ℒ= λdℒdata+ λpℒphysics+ λbcℒBC+ λicℒIC

Training minimizes the error against known data and the residual of the governing physical equations at once — so the model is both data-driven and physically consistent.

ℒdataData. Fit to experimental measurements and sensor histories.
ℒphysicsPhysics. Residual of balances, kinetics and transport equations.
ℒBC/ICConditions. Boundary and initial conditions of the domain.
Eq. 5
Governing physics · heat transfer
ρcp ∂T∂t + ρcp v·∇T = ∇·(k∇T) + Q

Automatic differentiation extracts the required derivatives directly from the network — embedding equations like the energy balance into the model rather than fitting around them.

Eq. 6
Prediction operator
x(t+τ)=D[x(t), u(t:t+τ), p]

After training, the PINN acts as a high-speed surrogate D — repeatedly computing the future state for any candidate control trajectory, enabling virtual experiments before touching the plant.

Digital twin

A living model, synchronized with the plant.

The PINN becomes the computational core of a digital twin — a dynamic representation continuously synchronized with the physical system through data exchange, throughout its life cycle.

Estimate

State estimation

Real-time estimation of the current process state, including variables that cannot be measured directly.

Predict

Process evolution

Prediction of how the process will develop under different candidate control actions.

Experiment

Virtual experimentation

Evaluate several scenarios and their consequences before applying any action to the physical system.

Identify

Parameter estimation

Recover process and equipment parameters that drift as conditions and feedstock change.

Detect

Anomaly detection

Compare predicted and measured behaviour; residuals flag sensor faults, degradation or abnormal regimes.

Optimize

Control & optimization

Feed prediction into an optimizer to select the action that best satisfies the process objectives.

Model Predictive Control

Evaluate every option before choosing one.

A trained PINN is fast enough to serve as the surrogate model inside a Model Predictive Control loop. For each candidate control trajectory it predicts the resulting future state — and the optimizer picks the best.

Current
state x(t)
→
u₁→PINN→x₁
u₂→PINN→x₂
u₃→PINN→x₃
uM→PINN→xM
→
Optimize J
→
Optimal u*
Process optimization

One objective, many criteria.

Industrial processes rarely have a single optimization criterion. The objective function balances competing goals simultaneously — optimizing overall process efficiency rather than any one parameter.

CriterionObjective
J_qualityMaximize product quality
J_energyMinimize energy consumption
J_productionMaximize productivity
J_stabilityMaintain stable operation
J_safetyKeep safe operating conditions
J_controlMinimize unnecessary control effort
Eq. 9
Optimal control action
u*= arg minu J(u)
Eq. 10
Weighted objective
J=w₁Jq+w₂Je+w₃Js+w₄Jsaf+w₅Jc

Weights wi encode the operator's priorities — the intelligent layer optimizes the process as a whole.

Applications

Built for nonlinear, coupled, thermochemical systems.

The approach is not tied to one type of equipment. It targets strongly coupled, dynamic industrial processes where behaviour is set by many interacting physical and chemical phenomena.

Thermochemical

Pyrolysis

  • Temperature distribution
  • Heat transfer
  • Feedstock conversion
  • Reaction kinetics
  • Gas composition
Gas processing

Gasification

  • Reactor modelling
  • Gas composition
  • Thermal-state estimation
  • Process optimization
  • Predictive control
Kinetics

Chemical reactors

  • Reaction kinetics
  • Transport equations
  • Process measurements
  • Predictive reactor models
High temperature

Thermal systems

  • Industrial furnaces
  • Heat-transfer systems
  • Thermal treatment
  • Energy systems
Worked example

A pyrolysis reactor, made predictable.

Pyrolysis is a complex thermochemical process — heating, moisture removal, decomposition, phase formation and secondary reactions. Many states can only be observed indirectly. A PINN combines those measurements with energy balances and kinetics to build a predictive digital twin of the reactor.

Reactor state vector
x = [ T, P, ṁ, Y, X, Q, … ]

Temperature, pressure, mass flow, product composition, conversion and thermal power — combined with energy and mass balances, heat-transfer and reaction-kinetics equations.

Before changing heating power
u₁→x₁, u₂→x₂, … , uM→xM

Each alternative is scored on production rate, energy consumption, product quality and compliance with process constraints — then the preferred control action is selected, ahead of the deviation.

Architecture

An AI layer that complements automation — not replaces it.

A modular cyber-physical stack. AI generates predictions and recommended actions; conventional control and protection systems keep operation within safe limits.

01Physical processSensors & actuators
02Data acquisitionProcessing & normalization
03Physics-Informed AI · PINN digital twinPrediction & estimation
04OptimizationMulti-objective J(u)
05Predictive controlRecommended actions
06PLC / SCADASafety & protection loops

└── control returns to the physical process · loop repeats on every measurement ──┘

Integration

Industrial protocols

PLC · SCADA · MQTT · OPC UA · Modbus · CAN/CANopen · Ethernet.

Deployment

Edge AI

Train on high-resource compute; deploy the trained PINN on an edge module close to the process for low-latency, real-time prediction.

Adaptation

Adaptive twins

New measurements refine model parameters over time as equipment ages and feedstock varies.

Why physics-informed AI

Engineering knowledge and AI — combined, not swapped.

→

Physics + data

Physical knowledge reduces dependence on purely empirical relationships and improves consistency.

→

Works with less data

Governing laws let the model operate with limited experimental data.

→

Fast surrogate

A trained PINN replaces computationally expensive physical models for repeated simulation.

→

Predicts the future

Evaluates future process behaviour instead of reacting only to current deviations.

→

Sees the unmeasured

Estimates hidden states — internal temperature, conversion, composition — from available data.

→

Optimizes many goals

Multiple technological criteria optimized simultaneously within one objective.

Engineering approach

From process understanding to intelligent control.

An engineering-oriented development sequence — each stage building on real process knowledge, not data alone.

01

Process analysis

Understanding the physical, chemical and technological structure of the process.

02

Data analysis

Evaluating available measurements, sensors, historical data and operating regimes.

03

Physical model

Identifying governing equations, constraints and process parameters.

04

PINN development

Constructing and training the Physics-Informed Neural Network.

05

Digital twin

Integrating the trained model into a dynamic digital representation.

06

Prediction

Validating future-state prediction across operating conditions.

07

Optimization

Developing multi-objective optimization algorithms.

08

Control

Integrating with predictive control and industrial automation.

09

Deployment

Deploying on industrial computing or edge platforms.

Research & publications

Grounded in peer-referenced science.

Featured research

Perspectives on the Application of Physics-Informed Neural Networks in Predictive Control Systems for Complex Technological Processes

D.Sc., Prof. Sergey Besedin · Inguz Navitas SIA, Riga · August 2026

The paper examines the prospects of applying PINNs to the modelling and predictive control of complex technological processes — combining machine learning with physical laws, experimental data and optimization. Using a pyrolysis reactor as an example, it demonstrates how a physics-informed model integrates into a closed-loop control system, and discusses advantages, application areas, limitations and directions for further development.

PINNPredictive controlDigital twinMachine learningPyrolysisOptimizationIntelligent control
13
Sections
7
References
10
Governing equations
R&D area

Hybrid physics-AI models

R&D area

Deep learning for physical systems

R&D area

Thermochemical modelling

R&D area

Model Predictive Control

FAQ

Physics-informed AI, explained.

Common questions about physics-informed neural networks, digital twins and predictive control for industrial processes.

A physics-informed neural network is a machine-learning model that embeds governing physical laws — differential equations, balances and boundary conditions — directly into training. It fits experimental data while satisfying the physics, producing a model that is both data-driven and physically consistent.

A trained PINN acts as a fast surrogate model inside a model predictive control loop. For each candidate control trajectory it predicts the resulting future state, and an optimizer selects the action that best satisfies the process objectives before it is applied to the plant.

A digital twin is a dynamic digital model continuously synchronized with a physical system through sensor data. With a PINN at its core it estimates the current state, predicts process evolution, detects anomalies and supports predictive control throughout the asset life cycle.

Yes. A PINN combines reactor measurements with energy and mass balances and reaction kinetics to predict temperature distribution, conversion and gas composition — building a predictive digital twin of the pyrolysis reactor for optimization and control.

A standard neural network learns only from data. A physics-informed neural network additionally enforces the residual of the governing physical equations, so it needs less data, generalizes better and stays physically consistent outside the training range.

Nonlinear, strongly coupled thermochemical and thermal systems: pyrolysis and gasification reactors, chemical reactors, industrial furnaces, heat-transfer and energy systems, and other processes where behaviour is set by interacting physical and chemical phenomena.

Team

Decades of thermophysics, behind the model.

Physics-informed AI is only as good as the physics behind it. Our work is grounded in a career of power-engineering research, computational fluid dynamics and thermochemical systems.

SB
Sergey Besedin
D.Sc., Prof. · Founder & Chief Scientist
Pescara, Italy · Inguz Navitas SIA, Riga

Scientist and research specialist in power engineering. In 2010 he created the first serial microturbine unit in Russia — a 20 kW microturbo-expander generator for gas distribution stations — and has since led the design of microturbines, ORC waste-heat recovery, cryogenic and supercritical-CO₂ power systems.

58
Publications
12
Patents
2
Monographs
35+
Years R&D
Computational Fluid Dynamics Thermal Physics Microkinetics Turbomachinery sCO₂ / Allam cycle Cryogenics
hello@inguznavitas.com
2021Doctor of Technical Sciences (D.Sc.)SPb State Polytechnical University — methodology of microturbine installations.
2011Candidate of Technical Sciences (PhD)100 kW microturbine generator — calculation & experimental methods.
1988Electronics Engineer — LETI, LeningradDiploma with honours (GPA 5.0 / 5.0).
Prof.Professor of Marine Power EngineeringSPb State Marine Technical University · CFD, fluid & gas mechanics.
HL
Helvijs Leja
Founder & CEO
Latvia · Inguz Navitas SIA

An experienced CEO and founder who builds and executes investable projects across real estate, energy and product development. At Inguz Navitas he leads strategy, partnerships and commercialization. More on his LinkedIn profile.

Real estate Energy Product development Investable projects
LinkedIn profile hello@inguznavitas.com +371 29185303
Contact

Let's build an intelligent model of your process.

Do you have a complex industrial process that is difficult to model, predict or optimize? We can help develop a physics-informed intelligent system from your process data and engineering knowledge.

Process modelling Digital twin development PINN development Predictive control Process optimization
Discuss your process

hello@inguznavitas.com · Riga, Latvia

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Last updated · 28 August 2026 Controller · Inguz Navitas SIA Jurisdiction · Latvia, EU (GDPR)