machine learning in engineering

Active learning is a machine learning approach in which the model actively requests the most informative new data points. In engineering, this can mean running additional simulations where model uncertainty is high or the engineering decision is especially important. This can generate data more efficiently than fixed experimental designs. Active learning is particularly interesting when individual simulations are expensive and every additional data point must be justified.

Adaptive sampling means that new simulation or test points are selected based on previous results. The model therefore does not only decide upfront, but learns during the process where additional data is most valuable. Points are often added in regions of high uncertainty, strong nonlinearity or close to an optimum. This can make surrogate models more accurate with fewer expensive CFD, FEA or test bench points.

AI-assisted product development describes the use of AI throughout the development process from concept to validation. It can structure requirements, accelerate simulations, evaluate variants, analyse test data and prepare engineering decisions. In CAE processes, it is especially useful when large datasets from DoE, CFD, test benches or operation are available. The greatest value arises when AI is combined with clear engineering targets, domain knowledge and traceable validation.

AI-assisted simulation uses artificial intelligence to make simulation processes faster, more robust or easier to evaluate. Examples include automated meshing, parameter selection, surrogate models, result prediction, error detection and fast approximation of expensive CFD or FEA calculations. AI is especially valuable when many operating points, geometry variants or optimization loops must be investigated. However, AI must be checked against physical references because a fast model is not automatically a correct model.

Artificial intelligence in engineering includes methods that analyse technical data, identify patterns, automate models or support decisions. This includes machine learning, optimization, image and signal analysis, language models, knowledge systems and automated postprocessing. In product development, AI can shorten development time, make simulation data more useful and evaluate variants more systematically. AI does not replace engineering expertise, but extends the toolchain when data quality, model limitations and validation are well controlled.

Bayesian optimization uses a probabilistic surrogate model to select expensive function evaluations as efficiently as possible. It is especially interesting when every CFD, FEA or test bench run is time-consuming. The method balances searching promising regions and exploring uncertain regions. In engineering applications, Bayesian optimization can be combined with Gaussian processes, Kriging or other surrogate models.

A boundary condition parameter describes a variable boundary condition of a simulation or data model. Examples include inlet pressure, mass flow rate, ambient temperature, vehicle speed, heat flux, rotational speed or turbulence level. In surrogate models, boundary condition parameters are important because a component can behave very differently depending on operating state. The valid range of these parameters must be clearly limited to avoid uncontrolled extrapolation.

A classification model assigns data points to fixed classes or categories. In engineering, it can distinguish between pass and fail, stable and unstable, healthy and faulty, or surge and no surge. Classification is useful when the goal is not an exact numerical value but a technical decision. Clear classes, balanced training data and evaluation of misclassification are important.

A constraint limits the solution space of an optimization. Examples include maximum packaging space, minimum wall thickness, allowable temperature, maximum pressure loss, strength limit, manufacturing restriction or regulation. Constraints are important so that the algorithm does not find unrealistic or non-manufacturable designs. Good optimization therefore needs not only objectives, but also clear engineering limits.

Data-driven modelling builds a model mainly from available data rather than from explicitly formulated physical equations. The data can come from simulations, measurements, test benches, vehicle operation or design of experiments. Such models are often fast and can approximate complex relationships if the application range is well covered by training data. Caution is required outside the data range because data-driven models can produce physically wrong predictions there.

Data preprocessing includes all steps that make raw data usable for machine learning. This includes cleaning, scaling, normalization, outlier checks, unit alignment, handling missing values and combining different data sources. In engineering, preprocessing is especially important because simulation and measurement data often have different formats, noise levels or boundary conditions. Poor preprocessing often leads to poor models, even when the algorithm itself is powerful.

A decision tree is a model that splits data through successive if-then decisions. It is easy to understand and can be used for both regression and classification. In engineering, it is useful for making simple decision rules or influencing variables visible. Single decision trees tend to overfit, however, and are often less robust than methods such as random forest or gradient boosting.

Deep learning refers to machine learning with deep neural networks. It is especially strong for large datasets, complex patterns and high-dimensional input data. In engineering, deep learning can be used for image processing, anomaly detection, field prediction, surrogate models and automated evaluation. Its technical value strongly depends on having enough representative data and clear validation metrics.

A deep neural network has multiple hidden layers and can therefore approximate very complex functions. It is especially suitable for large datasets, high-dimensional inputs, images, field data or complex surrogate models. In CAE contexts, deep networks can approximate flow fields, temperature fields or result metrics, for example. However, the effort for training, data preparation, regularization and interpretability is higher than for simple models.

Design exploration describes the systematic investigation of many design variants. The goal is to identify relationships, trends, sensitivities and possible optima in the design space. DoE, automated simulation, surrogate models and visualization are often combined for this purpose. In engineering, design exploration helps make better decisions before expensive hardware is built or test bench time is used.

Design of experiments, or DoE, is a structured planning method for simulations or experiments. The goal is to gain as much information as possible about influencing variables and target quantities with as few sample points as possible. In engineering, DoE is often used to build surrogate models, evaluate sensitivities or prepare optimizations. A good experimental design covers the relevant parameter space efficiently and avoids unnecessary computation or test bench time.

DoE is the abbreviation for design of experiments and describes the systematic selection of experiment or simulation points. In CAE processes, DoE is used to vary many parameters deliberately instead of selecting variants randomly or manually. This makes influencing variables, interactions and robust design regions visible. DoE is an important basis for surrogate models, response surfaces and automated optimization.

Design optimization improves an engineering design by deliberately changing design variables. Typical examples include duct geometries, cold plates, wing angles, intake runner lengths, component thicknesses or air guides. The goal is not only one better value, but a technically robust solution with good function, manufacturability and validation. CFD, FEA, DoE, surrogate models and optimization algorithms are often combined.

The design space is the part of the parameter space containing technically allowable design variants. It considers limits from packaging, manufacturing, cost, material, regulations, function and safety. In optimization, good or optimal solutions are searched within the design space. A clearly defined design space prevents an algorithm from proposing computationally attractive but technically unrealistic variants.

A design variable is a modifiable parameter of a design or simulation model. Examples include channel width, wing angle, radiator area, intake runner length, valve timing or component thickness. Design variables are varied deliberately in DoE, optimization and surrogate modelling. They should be chosen so that they are technically controllable and have relevant influence on the target variables.

An experimental design defines which parameter combinations are investigated in a test or simulation series. It determines how well the parameter space is covered and what conclusions can be drawn later. A good experimental design considers target variables, parameter limits, interactions, effort and statistical significance. In simulation, an experimental design can structure CFD runs, 1D models, FEA calculations or test bench experiments.

Feature engineering describes the deliberate creation, transformation and selection of input features for a machine learning model. In engineering, this can produce dimensionless numbers, ratios, combined geometry parameters or physically motivated surrogate quantities. A good feature can improve model quality more than a more complex algorithm. Feature engineering is especially valuable when engineering data is limited and physical prior knowledge can be used.

Feature extraction describes deriving meaningful features from raw data. From a flow field, for example, pressure loss, mass flow rate, vortex metrics, maximum temperature or integrated forces can be extracted. The goal is to condense complex data so that a model can learn relevant engineering relationships more easily. Good feature extraction combines data processing with technical domain knowledge.

A fractional factorial design investigates only a selected subset of all possible parameter combinations. This significantly reduces effort compared with a full factorial design. The trade-off is that some interactions can no longer be fully separated or can only be evaluated approximately. In engineering, a fractional factorial design is useful when many parameters must be considered but computation time or test bench time is limited.

A full factorial design investigates all combinations of the selected parameter levels. This allows main effects and interactions to be analysed very completely. The disadvantage is that the number of experiments or simulations grows strongly with each additional variable. Full factorial designs are therefore mainly suitable for few parameters or inexpensive calculations.

A Gaussian process is a probabilistic regression model that provides predictions together with uncertainty. This is especially useful in engineering because expensive simulations can be added selectively where uncertainty is high. Gaussian processes are often used for surrogate models, Bayesian optimization and small to medium-sized datasets. For very large datasets or very high dimensionality, however, they can become computationally expensive.

A genetic algorithm is an evolutionary optimization method using principles such as selection, crossover and mutation. It is suitable for nonlinear, discrete or difficult-to-differentiate problems. In engineering, it can be used for shape optimization, variant selection, parameter optimization or multi-objective optimization. The disadvantage is that many function evaluations may be required, so surrogate models or automated simulations are often helpful.

A geometry parameter describes a variable geometric property of a component or system. Examples include length, diameter, angle, radius, gap size, cross-section, curvature or position. In parametric CAE processes, geometry parameters are used to automatically generate and evaluate variants. For machine learning, they are important inputs when a model should predict the effect of design changes.

Global optimization searches for the best solution within the entire defined design space. It is important when many local optima exist or the objective function is strongly nonlinear. The effort is usually higher than for local optimization because more regions must be investigated. In engineering projects, global optimization is often used in early phases to identify good solution regions.

Gradient boosting is a method in which many weak models are gradually combined into a strong model. Each new tree corrects errors made by the previous models. In engineering, gradient boosting can provide very accurate predictions for tabular simulation and measurement data. It is powerful, but requires careful hyperparameter selection and validation to avoid overfitting.

Hybrid modelling combines physics-based models with data-driven methods. A typical example is a CFD or 1D model that is accelerated, corrected ols are especially interesting for surrogate models, digital twins, control, optimization and simulations with many variants.r supplemented by a machine learning model. This can combine physical plausibility with high computational speed. Hybrid mode

Influence analysis evaluates which input variables, boundary conditions or design variables change an engineering target quantity most strongly. It is closely related to sensitivity analysis, but is often used more generally for cause-effect evaluations. In engineering, it can show whether pressure loss depends more strongly on channel cross-section, roughness, volume flow or temperature, for example. A good influence analysis supports robust engineering decisions and avoids optimizing unimportant parameters.

An input parameter is a quantity passed into a model as an input. In engineering models, these can be geometry parameters, boundary conditions, material data, operating points or control variables. Input parameters define the case for which the model calculates a prediction. For surrogate models, all relevant input parameters must be clearly defined with meaningful value ranges.

Kriging is an interpolation and regression method often used in engineering surrogate models. It is closely related to Gaussian processes and can generate smooth response surfaces from limited sampling points. In engineering, Kriging is commonly used for DoE, optimization, sensitivity analysis and surrogate models of expensive simulations. Its advantage is good accuracy with few sampling points, while its disadvantages are modelling effort and sensitivity to data quality.

Latin hypercube sampling is a sampling method for efficiently covering a multidimensional parameter space. Each parameter range is divided into intervals so that each interval is represented as evenly as possible. This often achieves better coverage with fewer points than purely random sampling. In engineering, Latin hypercube sampling is commonly used for DoE, surrogate models and sensitivity analyses.

Linear regression describes a target quantity as a linear combination of input variables. It is simple, transparent and easy to interpret. In engineering, it is suitable for first trend analyses, simple correlations and robust baseline models. Its limitation appears for strongly nonlinear relationships, interactions or complex physical effects.

Local optimization improves a solution starting from one initial point and its neighbourhood. It is often faster than global optimization and can be very efficient when the starting point is already good. The disadvantage is that it can get stuck in a local optimum. In engineering, local optimization is often used for fine tuning after global search or engineering experience has identified a good design region.

A metamodel is a model built from the results of other models or experiments. It describes the relationship between parameters and results at a higher abstraction level. In CAE processes, a metamodel is often generated from a DoE with many CFD or FEA runs. It is used to analyse relationships faster, identify sensitivities and perform optimization more efficiently.

Model order reduction describes methods that reduce complex simulation models to a smaller and faster model form. The goal is to preserve the most important dynamic or physical properties. It is used when detailed models are too slow for optimization, control, real-time applications or large variant studies. The quality of model order reduction must always be checked against the original model or measurement data.

Multi-objective optimization considers several target quantities at the same time. In engineering tasks, objectives often conflict, such as low pressure loss, high heat transfer, low mass, low cost and good manufacturability. Instead of one single best solution, a set of good compromises is often obtained. These compromises are often shown using a Pareto front so engineers can select a technically meaningful solution.

A neural network is a machine learning model made of connected computational units called neurons. It can learn complex nonlinear relationships between inputs and outputs. In engineering, it is used for surrogate models, map replacement, image evaluation, sensor signals, condition monitoring and optimization. Neural networks can be very powerful, but require sufficient data, good scaling and careful validation.

Nonlinear regression describes relationships that cannot be captured by a simple linear function. In engineering, this is often the normal case, for example for flow resistance, heat transfer, material behaviour or efficiency maps. Nonlinear models can be much more accurate, but require more data and more careful validation. It is important that the chosen model form remains technically plausible and does not merely fit training data.

The objective function describes what an optimization algorithm should improve. It can minimize pressure loss, maximize heat transfer, reduce drag coefficient or increase efficiency, for example. With multiple targets, objective functions can be weighted or formulated as a multi-objective optimization. A poorly defined objective function often leads to computationally good but technically unusable solutions.

Optimization describes the systematic search for a better solution within a defined design space. In engineering, target quantities can include drag, pressure loss, maximum temperature, mass, efficiency or cost. Optimization always requires clear constraints and technically meaningful parameter limits. An algorithm only finds useful solutions when objective function, constraints and model accuracy are properly defined.

An optimization algorithm is a method that searches the design space for better solutions. Depending on the task, it can be gradient-based, evolutionary, stochastic, Bayesian or heuristic. The choice of algorithm depends on computation time, number of variables, nonlinearity, noise and constraints. In CAE projects, the algorithm alone is often not decisive, but its coupling with simulation, automation and validation.

An output variable is the result calculated or predicted by a model. In engineering, examples include drag, pressure loss, temperature, efficiency, stress, mass flow rate or component lifetime. Output variables can be scalar metrics or complete fields. A clear definition of the output variable is important so that training, validation and engineering interpretation are unambiguous.

The parameter space includes all possible combinations of a model’s input parameters. It defines the range in which a surrogate model, DoE or optimization model is intended to be valid. The more parameters are included, the more effort is required to cover the space sufficiently. In engineering, a meaningful limitation of the parameter space is important to keep models accurate, efficient and technically useful.

A parameter study deliberately investigates the influence of one or more parameters on an engineering result. It can be performed manually, automatically, simulation-based or measurement-based. In CAE projects, it is often used to identify trends, compare variants or check modelling assumptions. A good parameter study has clear target quantities, meaningful parameter limits and traceable evaluation.

A Pareto front shows solutions where one objective cannot be improved without worsening at least one other objective. It is especially useful for trade-offs such as downforce vs. drag, cooling performance vs. pressure loss or mass vs. stiffness. The Pareto front makes visible which designs are technically efficient and which are clearly dominated. For decisions, it is often more valuable than a single optimization value.

Physics-based modelling describes models based on physical equations, conservation laws and known material or fluid laws. Examples include CFD, FEA, 1D engine simulation and thermal networks. The advantage is better extrapolation capability when the relevant physical mechanisms are represented correctly. The disadvantage is often higher modelling effort, longer computation time and necessary assumptions about boundary conditions, material data and model parameters.

A physics-informed neural network, or PINN, combines neural networks with physical equations or constraints. The model learns not only from data, but is additionally guided by conservation equations, boundary conditions or known physical laws. This can produce more physically plausible solutions than a purely data-driven network when data is limited. PINNs are especially interesting for fluid flow, heat transfer, inverse problems and model reduction, but they are not automatically faster or simpler than classical simulation.

PINN stands for physics-informed neural network and describes a neural network that includes physical equations or constraints in addition to training data. The model is guided by conservation equations, boundary conditions, initial conditions or known material laws. This can make a PINN more physically plausible than a purely data-driven model when data is limited. In engineering applications, PINNs are especially interesting for fluid simulation, heat transfer, inverse problems and model reduction.

Polynomial regression extends linear regression with powers and interactions of input variables. This allows curved relationships to be described more easily. It is well suited for manageable response surfaces with moderate nonlinearity. With high polynomial order or many parameters, however, it can become unstable and strongly overfit.

Random forest is a machine learning method made of many decision trees. It can robustly represent nonlinear relationships and interactions. In engineering, it is suitable for regression, classification, feature importance and fast surrogate models. Its disadvantage is that random forests do not extrapolate smoothly and are often only partly reliable outside the training range.

A reduced order model, or ROM, is a simplified model with significantly reduced mathematical complexity. It aims to reproduce the essential behaviour of a detailed model with much shorter computation time. In engineering, ROMs are used for fluid flow, structures, thermal systems, control and digital twins. The key is that the reduction preserves the effects relevant to the engineering question and does not merely save computation time.

A regression model predicts continuous target quantities. In engineering, these can include drag, pressure loss, temperature, efficiency, stress or lifetime. Regression models learn from data how input variables relate to a numerical target quantity. They are especially suitable for surrogates, map replacement, trend analysis and fast predictions in optimization loops.

Response Surfaces sind gut verständlich, können aber bei stark nichtlinearen oder hochdimensionalen Zusammenhängen ungenau werden. | A response surface is a mathematical surface that describes the relationship between input parameters and a target quantity. It is often built from design of experiments or simulation data. In product development, it helps identify trends, optima and sensitivities quickly. Response surfaces are easy to understand, but can become inaccurate for strongly nonlinear or high-dimensional relationships.

A response surface model is a surrogate model that describes an engineering target quantity as a function of multiple input parameters. It is often used for DoE evaluation, optimization and variant comparison. Examples include drag over vehicle ride height and yaw angle or pressure loss over volume flow and geometry parameters. Model quality strongly depends on the selected sampling points and the chosen approximation function.

A sampling strategy describes how points in the parameter space are selected. It influences whether a model covers the design space uniformly, finds local optima or improves uncertain regions selectively. Examples include random sampling, Latin hypercube sampling, full factorial designs, adaptive sampling and active learning. A good sampling strategy saves computation time and improves the quality of surrogate models and optimizations.

Sensitivity analysis investigates how strongly input parameters influence a model’s target variables. It shows which parameters are important and which have little effect. In engineering projects, it helps prioritize design variables, reduce model complexity and better understand technical causes. Sensitivity analysis is especially valuable in combination with DoE, surrogate models and optimization.

Shape optimization changes the outer or inner shape of a component without completely changing its basic topology. In CFD projects, it can optimize radii, cross-sections, inlet shapes, diffuser angles, guide vanes or cooling channel paths. The advantage is that the resulting geometries often remain closer to the existing design. Shape optimization is especially useful when function should be improved without completely rebuilding packaging, manufacturing or interfaces.

A support vector machine is a method for classification and regression. It finds a decision boundary or regression function that describes data points with good separation or error control. With kernel functions, nonlinear relationships can also be captured. In engineering, it is useful for small to medium-sized datasets, but can become computationally expensive for large datasets.

A surrogate model is a fast replacement model for a slower, more expensive or more complex reference model. In engineering, it often replaces CFD, FEA, 1D simulation or test bench data in variant studies and optimization. The surrogate learns the relationship between input variables and target quantities from training data. Its validity range must be clearly defined because a surrogate model can become unreliable outside the trained data domain.

An Ersatzmodell is the German term for a surrogate model. It represents technical behaviour in a simplified and fast way without rerunning the full original simulation every time. Typical applications include aerodynamic maps, pressure loss models, heat exchanger maps, component optimization and system simulation. A good surrogate model is fast, sufficiently accurate and transparent regarding training data, error and validity range.

A target variable is the quantity that a machine learning model is intended to learn or optimize. In supervised learning, it is the reference value against which the model prediction is compared. In CAE projects, target variables can include drag coefficient, maximum cell temperature, pressure loss, downforce or NOx emission. The target variable must be technically meaningful, measurable or calculable and consistently defined across all data points.

Test data is used to evaluate model quality on previously unseen data. It should not be used for training or parameter selection so that the evaluation remains as independent as possible. In engineering, test data shows whether a surrogate model or regression model is reliable for new geometries, operating points or boundary conditions. A clear separation between training data, validation data and test data prevents overly optimistic results.

A test dataset is the separate dataset used to finally evaluate a completed model. It should contain representative cases that the model has not seen during training or validation. In CAE and engineering applications, the test dataset can consist of additional CFD runs, measurements or deliberately withheld DoE points. It provides the most important evidence of whether a model works reliably outside the training data.

Topology optimization searches for a favourable material distribution within a defined packaging space. It is often used for structural components, but can also be relevant for flow channels, cooling structures and additive manufacturing. The result often shows organic-looking geometries that must then be cleaned up and converted into manufacturable designs. Realistic load cases, boundary conditions and manufacturing constraints are essential.

Training data is the data used by a machine learning model to learn relationships. In engineering, it often comes from CFD simulations, FEA runs, test bench data, measurement series, DoE studies or operational data. The quality of the training data largely determines whether the model can make robust predictions later. Representative operating points, clean target values, consistent units and good coverage of the parameter space are important.

A training dataset is the structured collection of training data for a machine learning model. It contains input parameters, target variables and often additional metadata such as geometry version, simulation setup, boundary conditions or measurement uncertainty. For engineering models, not only the number of data points matters, but also their distribution in the parameter space. A good training dataset is traceable, cleaned and physically plausible.

Validation data is used during model development to select model variants, hyperparameters or training stopping points. It is therefore used for model selection, not for final independent evaluation. In engineering projects, validation data helps detect overfitting early and assess model quality in the relevant parameter range. The final statement about transferability should still be based on separate test data.

XGBoost is a widely used and efficient implementation of gradient boosting. It is often used for structured tabular data and frequently achieves high accuracy with relatively short training time. In engineering, it is suitable for surrogate models, fault classification, quality prediction and fast variant evaluation. As with all ML models, data quality, feature selection and validation are more important than the algorithm name itself.