This page presents my doctoral research proposal in full technical and methodological detail. The central problem is specific: when a trained machine learning model is embedded inside a Monte Carlo simulation used for techno-economic assessment, the sensitivity analysis you run on that simulation is no longer reliable in a way that current frameworks account for. My MSc thesis provides the mathematical foundation to fix this. The proposed doctoral work builds the fix, tests it, and delivers it as an open-source extension of the SimDec framework.
Something I kept running into during my MSc thesis work made more sense once I started reading techno-economic assessment literature seriously. My thesis examines the convergence behavior of adaptive gradient methods, specifically Adam and its variants, in high-dimensional parameter spaces. At some point it became clear to me that when you embed a trained neural network inside a larger simulation model, you are not just adding a fast predictive component. You are adding a component whose behavior depends on a training process that is stochastic, sensitive to initialization, and whose convergence properties are not carefully tracked in most applied modeling work. The model outputs carry uncertainty that does not come from the input parameters you are varying in your Monte Carlo runs. It comes from how the model learned.
The TEA literature dealing with clean energy and circular economy investments has increasingly adopted Monte Carlo simulation and global sensitivity analysis to unpack which uncertain inputs actually drive investment risk. The SimDec methodology, in particular, is well-suited to this because it preserves the scenario structure of sensitivity results rather than collapsing them to scalar indices. Applications in Power-to-X, waste management, and structural assessment have shown that this matters practically: identifying which combinations of uncertain inputs produce the worst outcomes is a different and more useful question than identifying which single input contributes most to variance. But the simulation models in this literature are built from explicit mathematical relationships. As ML surrogates increasingly replace these explicit components in applied TEA work, the uncertainty structure of the composite model changes in a way that current SimDec frameworks are not specifically designed to handle.
I am not suggesting the existing SimDec methodology is wrong. I am pointing to a gap that will become increasingly important as practitioners start embedding ML components in the simulation models they then subject to sensitivity analysis. The proposed research addresses that gap by extending SimDec's theoretical foundations to hybrid simulation-ML models, using the convergence analysis from my MSc thesis as the mathematical entry point.
ML surrogates are becoming standard in techno-economic assessment for a practical reason. High-fidelity physical models of processes like electrolysis, pyrolysis, material fatigue, or biological treatment are computationally expensive at the scale Monte Carlo analysis requires. A trained neural network that approximates the same input-output relationship runs faster by orders of magnitude, making large-scale uncertainty analysis feasible. This is a legitimate and useful development.
The problem is that the surrogate introduces a new category of uncertainty that is structurally different from the parametric uncertainties SimDec is designed to decompose.
Arises from imperfect knowledge of the model's input variables: investment costs, conversion efficiencies, market prices, policy parameters. This is what SimDec is designed to decompose. It is well-understood, quantifiable, and the entire point of running Monte Carlo analysis in the first place.
Arises from the training process of the ML model itself: stochasticity of mini-batch gradient descent, sensitivity to initialization, interaction between architecture choices and the loss landscape, and finite training dataset size. This is a fundamentally different kind of uncertainty, one that is not currently tracked or separated in any global sensitivity framework.
When you run SimDec on a simulation model containing an ML surrogate, the sensitivity indices you compute reflect both the input uncertainty you care about and the optimizer-induced noise you have not accounted for. In cases where convergence was incomplete or the surrogate operates near its training boundary, this distortion can be substantial enough to change which inputs appear to drive the outcome, leading to wrong investment priorities, wrong policy signals, and wrong research agendas.
There is currently no systematic framework for assessing when surrogate uncertainty matters and how to correct for it. That is the specific gap this research addresses.
The three questions below share a common thread: all of them are about understanding what optimizer-induced uncertainty does to a simulation model, and all of them require convergence theory and sensitivity analysis methodology to answer properly.
How does optimizer-induced stochasticity in trained ML surrogates propagate through a composite techno-economic simulation model, and how can its contribution to output variance be formally characterized using convergence-theoretic analysis?
Can SimDec be extended to decompose surrogate uncertainty separately from parametric input uncertainty, and what does a rigorous theoretical framework for this extension require?
In the context of sustainability-relevant investment decisions, does accounting for surrogate uncertainty materially change the sensitivity rankings and scenario structure that SimDec produces, and when is the correction practically significant?
The first question is the one I can make the fastest progress on, because it is a direct extension of the convergence work in my MSc thesis. The second and third depend on the results of the first. I expect the first year of doctoral work to be spent primarily on the theoretical framework, with the applied questions addressed in years two through four.
This research is the first to formally separate optimizer-induced uncertainty from parametric input uncertainty within a SimDec sensitivity decomposition framework, and to derive conditions under which ignoring the former materially distorts the latter.
The novelty sits at the intersection of three areas: the convergence theory of adaptive optimization algorithms, global sensitivity analysis methodology, and techno-economic modeling for sustainability transitions. No prior work connects all three.
Simulation Decomposition is a multi-dimensional sensitivity analysis tool that preserves scenario structure in a way that scalar Sobol indices do not. Applications in the published literature span energy systems, waste management, structural assessment, and technology investment decisions. What is not yet addressed is the hybrid case where part of the simulation is replaced by a learned function whose own uncertainty has a different structure.
Reviews by Bhosekar & Ierapetritou (2018) and Forrester & Keane (2009) cover surrogate-based optimization broadly. In energy systems, neural surrogates are increasingly used to make stochastic analysis tractable at system scale. The dominant motivation is computational efficiency. The question of how the surrogate's own uncertainty should be accounted for in sensitivity analysis is treated as secondary and in most cases not addressed formally.
Bayesian neural networks, Monte Carlo dropout (Gal & Ghahramani, 2016), conformal prediction, and deep ensembles quantify the uncertainty of a model's output given a new input. What they do not address is how that uncertainty interacts with external parametric uncertainty in a composite simulation model, and how it affects global sensitivity indices computed over that model.
Some work exists on Sobol indices for neural networks treated as black-box functions (Marrel et al., 2021; Saltelli et al., 2020). This is conceptually adjacent but does not address training-induced variance or connect to SimDec's multi-scenario structure. The convergence-theoretic angle of using analytical results about adaptive optimizers in high-dimensional non-convex settings to bound training-induced output variance has not been explored in this context.
The diagram below shows what happens inside a hybrid simulation-ML model and where the extended SimDec framework intervenes. The standard pipeline (left path) produces sensitivity indices that conflate two different sources of variance. The extended framework (right path) isolates them.
Using the convergence analysis from my MSc thesis as a foundation, I will develop a formal model of optimizer-induced variance propagation through a composite simulation-ML system. This involves characterizing the distribution of surrogate outputs as a function of optimizer parameters (step size, batch size, training iterations), loss landscape regularity conditions, and training dataset size. The goal is variance bounds that are tight enough to be informative and derived under assumptions realistic enough to apply to the surrogate models typically used in TEA.
The second step is developing the theoretical extension of SimDec's sensitivity decomposition to the hybrid model case. This requires working out how the standard variance decomposition interacts with a surrogate component whose variance has a structure given by the optimization analysis.
The second year translates the theoretical framework into tested computational tools. I will implement the extended SimDec framework in Python and R, building on the existing SimDec codebase. Validation will use synthetic benchmark problems where the ground truth is known, allowing the accuracy of the proposed correction procedures to be assessed directly.
The benchmark problems will be designed to span the range from cases where surrogate uncertainty is negligible to cases where it is large enough to change sensitivity rankings. This also tests the practical conditions derived in Phase 1: the analytical predictions about when Vopt matters will be verified numerically.
The third year applies the extended framework to Power-to-X systems. ML surrogates are already used in some Power-to-X models for electrolyzer performance and degradation approximation, making this a natural and realistic test case with existing published baseline models to build on (Karjunen et al., 2024).
The central question for this application is whether the sensitivity rankings produced by the standard SimDec approach change materially when surrogate uncertainty is properly accounted for. If the answer is yes in any realistic configuration, it implies that investment decisions and policy assessments based on existing TEA sensitivity analyses in this domain should be re-examined.
The fourth year applies the framework to circular economy investment models, where LCA models increasingly use ML components for process step approximation. The question of which uncertain inputs drive environmental and economic outcomes is directly relevant to sustainability policy. Applying the extended framework here tests whether the results generalize across application domains or whether domain-specific corrections are needed.
The year concludes with dissertation writing and defense, final journal submission, and the open-source release of the extended SimDec tools with full documentation for non-specialist users.
The convergence analysis work in my MSc thesis already produces the main building block. The code below sketches how optimizer-induced variance is characterized and then fed into an extended variance decomposition.
# Phase 1: Characterizing optimizer-induced variance in a trained surrogate # The convergence bound from MSc thesis gives: E[||θ_T - θ*||²] ≤ C · (σ²/T)^α # where σ² is gradient noise variance, T is training steps, α depends on loss geometry # This translates into a bound on surrogate output variance V_opt import numpy as np import torch from typing import Callable, Tuple def estimate_optimizer_variance( surrogate : torch.nn.Module, X_inputs : np.ndarray, # Monte Carlo input samples n_reruns : int = 50, # retrain from different seeds grad_noise_σ : float = None, # if None: estimated from training T_steps : int = None, ) -> Tuple[np.ndarray, float]: """ Returns: V_opt_per_sample : variance of surrogate output across reruns, per MC sample V_opt_bound : analytical upper bound from convergence theorem """ outputs = [] for seed in range(n_reruns): torch.manual_seed(seed) surrogate_copy = retrain_surrogate(surrogate, seed) preds = predict(surrogate_copy, X_inputs) outputs.append(preds) outputs = np.stack(outputs, axis=0) # (n_reruns, n_mc_samples) V_opt = np.var(outputs, axis=0) # empirical variance per sample # Analytical bound: V_opt ≤ L² · C(σ², T, d) where L is surrogate Lipschitz constant # C comes from the Adam convergence theorem (MSc thesis, Ch. 3) V_opt_bound = analytical_bound(grad_noise_σ, T_steps, dim=surrogate.param_count) return V_opt, V_opt_bound
# Phase 2: Extended SimDec: decomposing V(Y) = V_param + V_opt + V_interact # Builds on the existing SimDec R package; adds the V_opt correction layer extended_simdec <- function( Y_sim, # Monte Carlo outputs from hybrid model (vector, n_runs) X_param, # parametric input matrix (n_runs × n_inputs) V_opt_per_run, # surrogate variance estimate per MC run (from Python step) threshold = 0.05 # report warning if V_opt / V(Y) exceeds this ) { # Step 1: Standard SimDec on the full output simdec_raw <- simdec(Y_sim, X_param) # Step 2: Estimate V_opt contribution using convergence bounds V_total <- var(Y_sim) V_opt_mean <- mean(V_opt_per_run) ratio <- V_opt_mean / V_total if (ratio > threshold) { warning(sprintf( "Surrogate uncertainty accounts for %.1f%% of total variance. Sensitivity rankings may be distorted. Use corrected indices.", ratio * 100 )) } # Step 3: Corrected sensitivity indices (subtract V_opt from denominator) V_param <- V_total - V_opt_mean S_corrected <- simdec_raw$sensitivity_indices * (V_total / V_param) list( raw = simdec_raw, corrected_indices = S_corrected, V_total = V_total, V_param = V_param, V_opt = V_opt_mean, V_opt_ratio = ratio, ranking_changed = check_ranking_change(simdec_raw$sensitivity_indices, S_corrected) ) }
# Phase 3: Apply extended SimDec to a Power-to-X TEA model # Surrogate: neural network approximating electrolyzer stack degradation curve # Parametric inputs: capex, opex, electricity price, CO2 price, load factor, lifetime # Output: levelized cost of hydrogen (LCOH) distribution import numpy as np from scipy.stats import qmc import rpy2.robjects as ro from rpy2.robjects.packages import importr simdec_ext = importr("extended.simdec") # the Phase 2 R package param_dist = { "capex_eur_kw" : (400, 900), # uniform range "elec_price_eur_mwh": (20, 90), "co2_price_eur_t" : (30, 180), "load_factor" : (0.40, 0.95), "stack_lifetime_h" : (60000,100000), } # Quasi-random sampling for better coverage sampler = qmc.Sobol(d=len(param_dist), scramble=True) X = qmc.scale(sampler.random(100_000), [v[0] for v in param_dist.values()], [v[1] for v in param_dist.values()]) # Run hybrid model: explicit TEA equations + electrolyzer ML surrogate Y_lcoh = run_ptx_hybrid_model(X, surrogate=electrolyzer_nn) V_opt, _ = estimate_optimizer_variance(electrolyzer_nn, X) # Call extended SimDec via rpy2 result = simdec_ext.extended_simdec( Y_sim = ro.FloatVector(Y_lcoh), X_param = r_matrix(X), V_opt_per_run = ro.FloatVector(V_opt), threshold = 0.05 ) # Compare raw vs corrected rankings for the policy report # Key question: does co2_price look more dominant than it actually is # because the electrolyzer surrogate's optimizer noise inflated its apparent contribution? print_ranking_comparison(result["raw"], result["corrected_indices"])
By the end of the program, I aim to have completed at least three published papers and one open-source software release. Beyond the academic output requirements, there are applied and methodological contributions worth being explicit about.
Theoretically: a formal characterization of how training-induced variance in an ML surrogate propagates through a composite simulation model and affects SimDec sensitivity indices. This is new in the sensitivity analysis literature and provides the first convergence-theoretic basis for quantifying surrogate uncertainty in a GSA context.
Methodologically: an extended SimDec R package with documented conditions for when surrogate uncertainty can be safely ignored and correction procedures for when it cannot. Built for non-specialist TEA practitioners to use without mathematical background, applying the same standard I used when open-sourcing the MBA research pipeline.
Applied to clean energy: validated sensitivity analyses for Power-to-X TEA models with ML components, answering the question of whether existing published sensitivity rankings in this literature need to be revisited. Given the role Power-to-X is expected to play in the European energy transition, this has direct investment and policy relevance.
Conceptually: demonstrating that the convergence theory of ML optimizers is directly useful for something beyond algorithm design. Most work on adaptive gradient methods is motivated by wanting to make training faster or more stable. The proposed research shows that the same theoretical machinery produces practical guidance for applied modelers, a different kind of usefulness with direct policy relevance for sustainability decision-making.
The Nessling Foundation funds research that enables or supports sustainability transformation protecting natural systems. The proposed research connects to this theme through its application domain, not just its methods.
The stakes are concrete. Techno-economic assessment is how governments, energy agencies, and investors decide whether to commit to clean technologies: green hydrogen production, Power-to-X, circular economy systems, carbon capture. A national energy ministry deciding to prioritize one clean technology pathway over another on the basis of a TEA model that contains an unvalidated ML surrogate may be acting on sensitivity rankings that are structurally wrong. It may be concluding that carbon price uncertainty is the dominant risk driver when in fact electrolyzer efficiency uncertainty is, or vice versa, because the optimizer-induced noise in the surrogate has shifted the variance decomposition in ways that were never detected. That kind of error does not produce a wrong answer on paper; it produces wrong investment priorities in practice: wrong infrastructure built, wrong policy incentives set, wrong research agendas funded. For a sustainability transition that depends on getting the order of priorities right, this is not a theoretical concern. It is a practical one.
The problem will get worse before it gets better. As ML surrogates become standard in large-scale TEA, the number of models carrying this untracked variance layer will grow. The proposed research addresses the problem at the methodological level, producing a framework and open-source tools that practitioners can apply to any composite simulation-ML model before trusting its sensitivity results.
SimDec has been applied to sustainability investment problems in the published literature and has shown practical value in unpacking which uncertain factors actually drive outcomes. The proposed research extends that value to the next generation of TEA models. The intended beneficiaries are the researchers, analysts, and policymakers who use these tools to guide clean technology investment.
Bhosekar, A. & Ierapetritou, M. (2018). Advances in surrogate based modeling, feasibility analysis, and optimization: A review. Computers and Chemical Engineering, 108, 250–267.
Forrester, A. & Keane, A. (2009). Recent advances in surrogate-based optimization. Progress in Aerospace Sciences, 45(1–3), 50–79.
Gal, Y. & Ghahramani, Z. (2016). Dropout as a Bayesian approximation: Representing model uncertainty in deep learning. Proceedings of ICML 2016.
Karjunen, H., Kinnunen, S.K., Laari, A., Tervonen, A., Laaksonen, P., Kozlova, M. et al. (2024). Upgrading the toolbox of techno-economic assessment with SimDec: Power-to-X case. In Sensitivity Analysis for Business, Technology, and Policymaking, 228–253.
Kozlova, M., Moss, R.J., Roy, P., Alam, A. & Yeomans, J.S. (2024). SimDec algorithm and guidelines for its usage and interpretation. In Sensitivity Analysis for Business, Technology, and Policymaking Made Easy.
Marrel, A., Iooss, B. & Chabridon, V. (2021). The ICSCREAM methodology: Identification of penalizing configurations in computer experiments using screening and metamodel. Nuclear Science and Engineering, 195(4), 422–446.
Saltelli, A. et al. (2020). Five ways to ensure that models serve society: A manifesto. Nature, 582, 482–484.
Zaikova, A., Kozlova, M., Şenaydn, O., Havukainen, J., Astrup, T.F. et al. (2025). Decomposing uncertainty of greenhouse gas emission reduction costs in MSW management. Waste Management, 205, 115025.