Paper | Sieun Kim Portfolio

Unsupervised Conformal Novelty Detection for Hierarchical Data

Thu, 01 Jan 2026 00:00:00 +0000

Abstract

Electric vehicle (EV) battery packs exhibit a natural pack–module–cell hierarchy, which induces dependence among measurements within the same module. Such hierarchical dependence poses challenges for the direct application of conventional novelty detection methods. To address these challenges, we develop conformal e-value procedures for hierarchical novelty detection, with the goal of controlling the false discovery rate (FDR) at both the group and unit levels. We combine hierarchical conformal score construction with eBH and U-eBH multiple testing procedures, and consider split conformal, full conformal, and group-wise conformal regimes. The proposed methods are evaluated through simulation studies and an analysis of EV battery pack data, where they provide empirical FDR control and detect localized module- and cell-level irregularities.

Type

Preprint

Publication

To be submitted to Journal of the Korean Statistical Society (JKSS, SCIE)

Keywords

novelty detection · hierarchical structure · conformal inference · false discovery rate · multiple testing

Motivation

Real-world industrial data — such as EV battery manufacturing — presents three compounding challenges that standard anomaly detection cannot handle jointly:

Hierarchical dependence: Cells within the same module share a common group effect, violating the IID assumption of most methods.
No anomaly labels: Ground-truth defect labels are expensive or infeasible to obtain in manufacturing, ruling out supervised approaches.
Multiple comparisons: Simultaneously testing hundreds of units inflates false discoveries without a principled error-control mechanism.

Method Overview

We frame hierarchical novelty detection as a multiple hypothesis testing problem at two levels simultaneously:

Group-level (HC-GND) — Does a test module contain any anomalous cells?
Unit-level (HC-UND) — Which specific cells within each module are anomalous?

Feature extraction: Charging voltage time series are treated as functional observations. Functional PCA (FPCA) projects each cell’s charging curve onto a low-dimensional score vector, placing cells from all packs on a common feature space.

Preprocessed charging voltage curves for all cells in the six test packs. Normal packs (blue) show regular charging behavior; Abnormal packs 4 and 5 (red) exhibit irregular patterns that are difficult to distinguish visually at the pack level.

Two-dimensional FPCA score vectors under the split conformal regime. Normal reference packs (black) form a tight cluster, while abnormal test packs (red) appear in a distinct region, validating FPCA as a discriminative feature extraction step.

Nonconformity score: For each cell, we compute a Mahalanobis-distance-based nonconformity score relative to a robust trimmed-mean group center. This naturally respects within-group dependence.

Multiple testing: Scores are converted to conformal e-values — non-negative statistics satisfying E[e] ≤ 1 under the null — and tested jointly via the eBH / U-eBH procedure, guaranteeing FDR control under minimal distributional assumptions.

We implement three conformal regimes with different data-efficiency / robustness trade-offs:

Regime	Training data	Contamination risk	Theoretical FDR guarantee
HSC (Split)	Reference only	None	✓ Both levels
HFC (Full)	Reference + all test	Higher	✓ Group level
HGC (Group-wise)	Reference + one test group	Moderate	✓ Group level

Results

Simulation Study

HC-GND simulation results. Empirical FDR (top) and power (bottom) under varying outlier proportions (left) and signal strengths (right). All three regimes maintain FDR below the target α = 0.1. HFC and HGC achieve higher power than HSC, especially at low outlier proportions, by exploiting more calibration data.

HC-UND vs. non-hierarchical baselines. The proposed hierarchical methods (HSC, HFC, HGC) consistently outperform non-hierarchical counterparts (SC, FC, AdaDetect) in power while maintaining empirical FDR control. Unit-level anomalies that are subtle in the pooled population become detectable within their own group context.

Key findings across 1,000 simulation replicates (α = 0.1):

Empirical FDR remains at or below the target level across all outlier proportions and signal strengths.
At weak signal, power reaches ~40%; as signal increases, power approaches 100%.
Hierarchical methods outperform non-hierarchical baselines by leveraging within-group structure.

EV Battery Pack Application

Pack-wise detection results (α = 0.1). Left three columns: hierarchical HC-GND/HC-UND results (yellow = module rejection, red = cell rejection). Right three columns: non-hierarchical baselines (SVM, Isolation Forest, AdaDetect). The proposed methods identify localized irregularities in Abnormal Pack 5 across multiple modules and cells that non-hierarchical methods largely miss.

The proposed procedures detect localized module- and cell-level irregularities not captured by pack-level labels.
Non-hierarchical baselines concentrate false detections on Normal Pack 0 and miss structured signals in Abnormal Pack 5.
Results provide an additional diagnostic layer when only coarse pack-level labels are available.

Presentation Slides

Multi-Agent Large Language Model-Based Economic Dispatch Framework for Optimal Energy Management of Data Center Microgrids

Thu, 01 Jan 2026 00:00:00 +0000

Abstract

The rapid expansion of artificial intelligence (AI) workloads and cloud computing drives a significant rise in hyperscale data centers. This growth in power demand, coupled with extreme load volatility inherent to AI operations, severely destabilizes power grids and complicates energy management. Consequently, data centers increasingly evolve into localized microgrids equipped with distributed energy resources (DERs) and energy storage systems (ESS). However, conventional economic dispatch models—typically based on Mixed-Integer Linear Programming (MILP)—demand specialized optimization expertise and make it difficult to respond flexibly to dynamic business environments, often requiring time-consuming model redesigns whenever tariffs (e.g., Time-of-Use rates) or environmental regulations (e.g., Renewable Energy Certificates) change.

To address these challenges, this paper proposes a multi-agent large language model (LLM)-based economic dispatch framework for data center microgrids. The model operates through a four-stage sequential agent architecture that lets operators execute complex optimization tasks from natural-language inputs. The efficiency of the framework is validated through simulations using the MIT TX-GAIA data center load profile scaled to 400 MW, configured with small modular reactors (SMR), gas turbines (GT), photovoltaics (PV), and a BESS.

Type

Conference

Publication

To be submitted to CIRED 2026

Demo

Interactive Streamlit app ↗

Keywords

LLM agent · economic dispatch · data center microgrid · energy management · multi-agent system

Motivation

AI workloads are pushing hyperscale data centers toward extreme, volatile power demand that destabilizes grids. To stay reliable and cost-efficient, data centers are becoming localized microgrids with distributed energy resources and storage. But the conventional way to operate them has real barriers:

High expertise barrier: MILP-based economic dispatch requires specialized optimization and modeling skills that facility operators rarely have.
Rigid to change: Whenever tariffs (Time-of-Use rates) or regulations (Renewable Energy Certificates) change, the entire model often needs a slow, complete redesign.
Slow scenario testing: Validating “what-if” operational strategies is time-consuming under rigid formulations.

System Configuration

The target is a grid-connected hyperscale data center microgrid sized for AI workloads.

Component	Parameter	Value
Data Center Load	Peak load	400 MW (AI/HPC workload)
SMR	Unit capacity / ramp / cost	100 MW · 0.75 MW/15 min · ≈ 7 USD/MWh
Gas Turbine (GT)	Unit capacity / ramp / fuel	170 MW · 15 MW/min · LNG
ESS	Energy / power / efficiency / SOC	160 MWh · 40 MW · 95% · 10–90%

Load modeling. The MIT Supercloud TX-GAIA HPC dataset — chosen for its high volatility relative to commercial data centers — was normalized from its native 300 kW scale up to a 400 MW peak and resampled to a 15-minute resolution (96 steps over 24 hours):

$$P_{load}(t) = \frac{P_{raw}(t)}{P_{raw}^{max}} \times 400\ \text{MW}$$

Generator modeling. The GT uses a quadratic cost function $C_{GT}(P) = aP^2 + bP + c$ (derived via GasTurb at 800 KRW/kg LNG) capturing partial-load efficiency drop, with a 15 MW/min ramp limit. The SMR (SMART-100, 100 MW) operates as baseload at 7 USD/MWh with a strict 0.75 MW/15 min ramp limit for operational safety.

Method Overview

We propose a four-stage sequential multi-agent LLM pipeline that converts a natural-language prompt into an optimized dispatch schedule — no manual model rebuilding required.

Four-stage agent architecture. An infeasibility-feedback loop returns from the solver to the formulation agent when constraints cannot be satisfied.

Parsing Agent — extracts optimization parameters from the user’s natural-language prompt.
Formulation Agent — translates the parameters into a formal mathematical model (objective + constraints).
Solver Agent — executes the computational dispatch and returns the optimal schedule.
Explanation Agent — synthesizes the numerical results into a comprehensive, human-readable strategic report.

A feedback loop returns infeasibility signals from the solver back to the formulation stage, enabling automatic correction without operator intervention.

Mathematical Formulation

Objective — minimize total daily operational cost $J$ (base demand charge + generation + grid purchase − sales revenue + ESS degradation):

$$\min J = C_{base} + \sum_{t=1}^{T} \Big[ \sum_{i \in \mathcal{G}} C_{gen,i}(P_i(t)) + \rho_{grid}(t)P_{grid}(t) - R_{sales}(t) + \sum_{k \in \mathcal{E}} \lambda_{deg} P_{dis,k}(t) \Big]$$

Key constraints:

Power balance — supply equals demand at every step $t$ (grid + generators + PV + ESS discharge = load + ESS charge).
ESS dynamics — $SOC(t) = SOC(t-1) + \big(P_{chg}(t)\eta - P_{dis}(t)/\eta\big)\Delta t / E_{cap}$, with round-trip efficiency $\eta = 0.95$ and $10\% \le SOC(t) \le 90\%$.
Generator limits — capacity bounds $P_{min,i} \le P_i(t) \le P_{max,i}$ and ramp limits $|P_i(t) - P_i(t-1)| \le Ramp_i$.

The Solver Agent casts this as a Mixed-Integer Quadratic Program (MIQP) and solves it with Gurobi for the global cost-minimizing optimum.

Results

The framework was validated on the MIT TX-GAIA data center load profile scaled to 400 MW over a 24-hour horizon, with a portfolio of small modular reactors (SMR), gas turbines (GT), photovoltaics (PV), and a BESS.

Key findings:

SMR as baseload: The framework seamlessly utilizes the SMR for stable baseload supply (~121 MW average, capacity factor ~100%).
Peak shaving: ESS and gas turbines are dispatched strategically for peak shaving during expensive TOU periods.
Cost structure: Total cost was driven primarily by dispatch strategy — baseload generation accounted for only ~2.5% of total cost, while variable operating cost dominated at ~90.9%, confirming that operational decisions matter more than raw asset mix.
Interactive testbed: The pipeline serves as a rapid, interactive testbed for verifying strategies against uncertainties in cost, load dynamics, and grid stability — and scales to other load systems.

Future Work

Capacity optimization: Move from fixed capacities to optimal sizing of GTs and ESS for a given load profile.
PV curtailment & RE100: Add objective penalty terms for curtailed renewables and minimum-usage constraints to meet sustainability targets.
Conformal prediction: Integrate distribution-free prediction intervals with guaranteed coverage into the demand-forecasting module, letting the Formulation Agent build uncertainty-aware robust optimization models that hedge against AI-workload volatility — reducing the risk of shortage or over-generation.

Try the Live Demo

The full agent pipeline is deployed as an interactive web app. Enter a natural-language scenario and watch the agents parse, formulate, solve, and explain the optimal dispatch in real time.

🚀 Launch the Streamlit App